2024年11月23日土曜日

Snapshot in my brain : [1]World with c(G1,G2,G3)...

Hi.
[1]pの世界で、隣接する者たち。mod(P(n),6)の世界にようこそ。
[2]P(n).vs.P(n+1)で、mod(P,6)=c(1,5)をG1と呼ぼう。同じくc(5,1)はG2。最後にc((1,1),(5,5))をG3だ。
[3]初めは、それぞれ別の世界で生きていた。しかし、実はお互いに関係したのだ。戦いではなく、共存だ!世界平和を今ここに。
[4]図形でいうと、[a]直線系、[b]三角形の2つからなり、(G1,G2,G3)の関係が絡みつつ、周期的に前に進む。
  • 着目するもの(着目物)として、G1,G2,G3のいずれか1つに決める。例)着目物=G1.
  • 着目物以外のG?で、着目物を挟むペアを探す。例)G2,G3で、G1を挟む直近のペアを探す。
  • 着目物、そのペアの関係、ペア間の関係で、Pが重なる関係を見ていく。
  • 例)関係は、[a]直線系:G1=G2=G3,G1=G2-G3,G1=G2,とか、[b]三角形:△(各頂点にG?を配置)とかが見える。
[5]では、具体的に見ていこう。まずは手書きだが、一覧を示す。誤りなければ...
[P=5 to 113]
  • P(=n)=7は、着目物(based)=G1、両端にG2(二重結合)。G3は、P=7以前なし、P=7以降G2と接していないので、<>G3。表記的には、形の欄だが、直線系:G1=G2.
  • P=17 : based=G2.両端=G1.P=17以前n=5がG2なので、一旦切れる。P=17以降G1とG3が隣接。表記として、直線系:G2=G1-G3(二重結合と一重結合).
  • P=19 : based=G1.両端=c(G2,G3).P=19以前n=13がG1なので、切れ。paired(G2)=c(17,29).P=19以降G3とG2が隣接。表記は、三角形:△(各頂点にG1,G2,G3),全て一重結合。
  • 三角形にも、一部、二重結合あり。P=67 : based=G1.両端=c(G3,G2).更にその外側でG2,G3が隣接。表記は、三角形:△,G2=G3.
  • 直線系にもすべて二重結合あり、P=41 : based=G2.両端=G1(二重結合). 更にその外側で、G1とG3が隣接。表記は、G2=G1=G3(全て二重結合).
[P=113 to 269]
  • P=257 : G3単独が現れた...?
[P=269 to 433]
  • 似たようなパターンが続く...
[6]つらつら眺めると、ルールは未確定ながら、ストーリー的に語るとこうなる。順不同。
  • △が続くと、中は二重結合になる。3以上で、中1つ。4つで、中2つ?
  • 直線系:G1(based)=G2-G3の場合、次のbased=G2,G3と続く。続かない場合、そこでパターンが切れる。
  • 直線系:G1=G2の場合、次はG2=G1,G1=G2と、basedが続いていく。続くまで、同一パターンとして見れる。
  • P=c(41,43,47) : basedは違うが、同一パターンをみなせる? G2-G1-G3.(正転、反転、結合二重、一重を無視すれば)。
  • G?=G?=G?がピーク?、後は結合は1段階ずつ落ちていく? G?=G?=G? to G?=G?-G? to G?-G?-G?. とか。
  • 直線系と三角形の関係?:直線系:(G?-G? to G?-G?-G?:直2 to 直3)の後に、三角形:△が出現?
  • パターンは、P的に3つ/or/6つ?
  • (つぶやき)周期はあるのか?/or/基本セットが様々な組み合わせで、単純結合しているだけなのか?
  • 続く/or/...
return(false).

2024年8月1日木曜日

Fake or Real? : Prime Gap...with mod(6)...clustering...

[1]連続するP間のギャップを見てみる。gap=diff(Pn, Pn+1)
[2]mod(6)で、グループ分けする。mod(6,Pn).vs.mod(6,Pn+1)
[3]G1=(1,5), G2=(5,1), G3=((1,1),(5,5)), G?=(mod(6,Pn), mod(6,Pn+1))
[4]gapとdiffを混在して使用しています。
[5]G1: diff=6n+4, G2 : diff=6n+2, G3 : diff=6n+0
[6]ギャップの傾向をみるために、その値が始めて出たとき、ギャップと、その素数を見てみる。
参考サイト:http://www.asahi-net.or.jp/~kc2h-msm/pbsb/pbsbm006.htm
同サイトから抜粋。
[7]G1のgap傾向をみる。ざっくり版として。
オリジナルデータのトレンド傾向をもとに、係数を変更して上限、下限のラインでデータが収まるようにする。

[8]G2のgap傾向も同様にみる。

[9]G3のgap傾向もみる。

[10](TODO)各グループでの範囲を限定して、トレンド線の上限・下限を見極めたい。
end.

2024年7月5日金曜日

Fake or Real? : Prime number test...

[1]N is prime(p) or not?

[2]mod(N,6)=c(1,5) is target.but included c(p,!p)

[3]素数判定:約分:c(2:sqrt(N))で、mod()=0, !0

~~~

[4]例)N=375,397,013=(9,923)*(37,831)=p1*p2, sqrt(N)=19375.164...int()=19,375

[5]log6(375397013)=11.01...

[6]x=6 : N=x^11+...+0*x^6+0*x^5+...+5

[7][5]=11/2=5.5; see c(x^5:x^6), x=6 : x^5=7,776, x^6=46,656

[8]素数判定の範囲 : range=c(x^5:int(sqrt(N)))=c(7,776 : 19,375)=(直下A:A)

~~~

[9]x=6は妥当か?:Is x=6 valid?

[10]to be ckecked : x=c(2:10)

[11]x=2 : logx(N)=28.48/2~14 : x^(13,14,15)=c(8192, 16384, 32768) : range=c(16384 : 19375) : diff=2991 : p1=out of range~p1=out;(see [4])

[12]x=3 : logx(N)=17.97/2~8.5 : x^(8,9)=c(6561, 19683) : range=c(6561 : 19375) : diff=12814 : p1 in range~p1=in;

[13]x=4 : logx(N)=14.24/2~7 : x^(6,7,8)=c(4096, 16384, 65536) : range=c(16384 : 19375) : diff=2991 : p1=out;

[14]x=5 : logx(N)=12.26/2~6 : x^(5,6,7)=c(3125, 15625, 78125) : range=c(15625 : 19375) : diff=3750 : p1=out;

[15]x=6 : logx(N)=11.01/2~5.5 : x^(5,6)=c(7776, 46656) : range=c(7776 : 19375) : diff=11599 : p1=in;

[16]x=7 : logx(N)=10.14/2~5 : x^(4,5,6)=c(2401, 16807, 117649) : range=c(16807 : 19375) : diff=2568 : p1=out;

[17]x=8 : logx(N)=9.49/2~4.5 : x^(4,5)=c(4096, 32768) : range=c(4096 : 19375) : diff=15279 : p1=in;

[18]x=9 : logx(N)=8.98/2~4 : x^(3,4,5)=c(729, 6561, 59049) : range=c(6561 : 19375) : diff=12814 : p1=in;

[19]x=10 : logx(N)=8.57/2~4 : x^(3,4,5)=c(1000, 10000, 100000) : range=c(10000 : 19375) : diff=9375 : p1=out;

~~~

[20]in c([11]:[19]) : {p1=in & min(diff)} is x=6

bye.

2023年1月3日火曜日

Garbage? : bye-bye pow()...

[1]廃棄関連に、pow()があった。何か最後に生かせるか? 今年最後の数遊び!
[2]pow()は、2018年にやっていた。pow()は、(python org shell)で実行。
____pow(123,456,789)=mod(123^456, 789), pow()=べき剰余。
[3]やはり、手持ちのborder()=関連の情報とで、何か知見を得られないかになる。
border3つ組 for pow(a,b,c)
a=init,
c=max(border)
pow(a,b=c(a:c),c)
what's to be happened?
(2,7,11)pow(2,c(2:11),11)around pow(2,7,11)?
(5,7,8,11)init=5
(5,c(5:11),11)*n, n=c(1,2,3,...)
---
n=1:pow(5:c(5:11),11)
n=2:pow(10,c(10:22),22)
n=3:pow(15,c(15:33),33)
around pow()/n?
__pow(5,7,11)?
__pow(5,8,11)?
(11,19,29)pow(11,c(11:29),29)
around pow(11,19,29)?
((0.8),5,8,11)init=0.8,ceiling(init)=1
(1,5,8,11),
1^n=1,pow():meaningless
(1,b,11)*n, n=c(2,3,4...)
---
n=2:pow(2,c(2:22),22)
n=3:pow(3,c(3:33),33)
n=4:pow(4,c(4:44),44)
around pow()/n?
__pow(1,5,11)?
__pow(1,8,11)?
(29,41)init=?
use 19 in (11,19,29),
---
pow(19,c(19:41),41)
around pow(19,29,41)?

[4]pow(a,b,c)=
___pow()=which pos(?--a--b--c--?)
___pow()=which pos(out(a,ab)--a--in(ab:?%)-b--in(bc:?%)--c--out(c,bc))
___3つと1つの数字の世界で見て何が起こっているか? pow()の処理系は忘れる、知らないものとする。

[5]pow(2,c(2:11),11)
pow(2,n,11)poscomment
>>> pow(2,2,11)
4
@in bc:(4-2)/(11-2)=22.22%
@in ac:(4-2)/(11-2)=22.22%
(bc->?)
>>> pow(2,3,11)
8
@in bc:(8-3)/(11-3)=62.5%
@in ac:(8-2)/(11-2)=66.67%
(bc->bc)
>>> pow(2,4,11)
5
@in bc:(5-4)/(11-4)=14.28%
@in ac:(5-2)/(11-2)=33.33%
(bc->bc)
>>> pow(2,5,11)
10
@in bc:(10-5)/(11-5)=83.33%
@in ac:(10-2)/(11-2)=88.88%
(bc->bc)
>>> pow(2,6,11)
9
@in bc:(9-6)/(11-6)=60%
@in ac:(9-2)/(11-2)=77.77%
(bc->bc)
>>> pow(2,7,11)
7
@b, @in ab:100%,@bc:0%
@in ac:(7-2)/(11-2)=55.55%
(bc->ab),changed
1st:nearest(50%)
>>> pow(2,8,11)
3
@in ab:(3-2)/(8-2)=16.67%
@in ac:(3-2)/(11-2)=11.11%
(ab->ab)
>>> pow(2,9,11)
6
@in ab:(6-2)/(9-2)=57.14%
@in ac:(6-2)/(11-2)=44.44%
(ab->ab)
>>> pow(2,10,11)
1
@out a, @out ab:(2-1)/(10-1)=11.11%
@in ac:---%
(out:ignored)
>>> pow(2,11,11)
2
@a, @in ab:0%
@in ac:0%
(ab->ab)

[6]pow(11,c(11:29),29)
pow(11,n,29)poscomment
>>> pow(11,11,29)
10
@out a, @out ab:(11-10)/(11-10)=100%
@in ac:---%
(out:ignored)
>>> pow(11,12,29)
23
@in bc:(23-12)/(29-12)=64.7%
@in ac:(23-11)/(29-11)=66.66%
(bc->?)
>>> pow(11,13,29)
21
@in bc:(21-13)/(29-13)=50%
@in ac:(21-11)/(29-11)=55.55%
(bc->bc)
1st:50%
1st:near(55.55%)
>>> pow(11,14,29)
28
@in bc:(28-14)/(29-14)=93.33%
@in ac:(28-11)/(29-11)=94.44%
(bc->bc)
>>> pow(11,15,29)
18
@in bc:(18-15)/(29-15)=21.42%
@in ac:(18-11)/(29-11)=38.88%
(bc->bc)
>>> pow(11,16,29)
24
@in bc:(24-16)/(29-16)=61.53%
@in ac:(24-11)/(29-11)=72.22%
(bc->bc)
>>> pow(11,17,29)
3
@out a, @out ab:(11-3)/(17-3)=57.14%
@in ac:---%
(out:ignored)
>>> pow(11,18,29)
4
@out a, @out ab:(11-4)/(18-4)=50%
@in ac:---%
(out:ignored)
50%
>>> pow(11,19,29)
15
@in ab:(15-11)/(19-11)=50%
@in ac:(15-11)/(29-11)=22.22%
(bc->ab),changed
1st:50%
>>> pow(11,20,29)
20
@b, @in ab:100%, @in bc:0%
@in ac:(20-11)/(29-11)=50%
(ab->bc),changed?
(ab->ab)
2nd:50%
>>> pow(11,21,29)
17
@in ab:(17-11)/(21-11)=60%
@in ac:(17-11)/(29-11)=33.33%
(bc->ab),changed?
(ab->ab)
>>> pow(11,22,29)
13
@in ab:(13-11)/(22-11)=18.18%
@in ac:(13-11)/(29-11)=11.11%
(ab->ab)
>>> pow(11,23,29)
27
@in bc:(27-23)/(29-23)=66.66%
@in ac:(27-11)/(29-11)=88.88%
(ab->bc),changed
>>> pow(11,24,29)
7
@out a, @out ab:(11-7)/(24-7)=23.5%
@in ac:---%
(out:ignored)
>>> pow(11,25,29)
19
@in ab:(19-11)/(25-11)=57.14%
@in ac:(19-11)/(29-11)=44.44%
(bc->ab),changed
>>> pow(11,26,29)
6
@out a, @out ab:(11-6)/(26-6)=25%
@in ac:---%
(out:ignored)
>>> pow(11,27,29)
8
@out a, @out ab:(11-8)/(27-8)=15.78%
@in ac:---%
(out:ignored)
>>> pow(11,28,29)
1
@out a, @out ab:(11-1)/(28-1)=37.03%
@in ac:---%
(out:ignored)
>>> pow(11,29,29)
11
@a, @in ab:0%
@in ac:0%
(ab->ab)

[7]pow(19,c(19:41),41)
pow(19,n,41)poscomment
>>> pow(19,19,41)
28
@in bc:(28-19)/(41-19)=40.9%
@in ac:(28-19)/(41-19)=40.9%
(bc->?)
>>> pow(19,20,41)
40
@in bc:(40-20)/(41-20)=95.2%
@in ac:(40-19)/(41-19)=95.45%
(bc->bc)
>>> pow(19,21,41)
22
@in bc:(22-21)/(41-21)=5%
@in ac:(22-19)/(41-19)=13.63%
(bc->bc)
>>> pow(19,22,41)
8
@out a, @in ab:(19-8)/(22-8)=78.5%
@in ac:---%
(out:ignored)
>>> pow(19,23,41)
29
@in bc:(29-23)/(41-23)=33.3%
@in ac:(29-19)/(41-19)=45.45%
(bc->bc)
>>> pow(19,24,41)
18
@out a, @in ab:(19-18)/(24-18)=16.67%
@in ac:---%
(out:ignored)
>>> pow(19,25,41)
14
@out a, @in ab:(19-14)/(25-14)=45.45%
@in ac:---%
(out:ignored)
>>> pow(19,26,41)
20
@in ab:(20-19)/(26-19)=14.2%
@in ac:(20-19)/(41-19)=4.54%
(bc->ab),changed
>>> pow(19,27,41)
11
@out a, @in ab:(19-11)/(27-11)=50%
@in ac:---%
(out:ignored)
50%
>>> pow(19,28,41)
4
@out a, @in ab:(19-4)/(28-4)=62.5%
@in ac:---%
(out:ignored)
>>> pow(19,29,41)
35
@in bc:(35-29)/(41-29)=50%
@in ac:(35-19)/(41-19)=72.72%
(ab->bc),changed
1st:50%
>>> pow(19,30,41)
9
@out a, @in ab:(19-9)/(30-9)=47.6%
@in ac:---%
(out:ignored)
>>> pow(19,31,41)
7
@out a, @in ab:(19-7)/(31-7)=50%
@in ac:---%
(out:ignored)
50%
>>> pow(19,32,41)
10
@out a, @in ab:(19-10)/(32-10)=40.9%
@in ac:---%
(out:ignored)
>>> pow(19,33,41)
26
@in ab:(26-19)/(33-19)=50%
@in ac:(26-19)/(41-19)=31.81%
(bc->ab),changed
2nd:50%
>>> pow(19,34,41)
2
@out a, @in ab:(19-2)/(34-2)=53.12%
@in ac:---%
(out:ignored)
>>> pow(19,35,41)
38
@in bc:(38-35)/(41-35)=50%
@in ac:(38-19)/(41-19)=86.36%
(ab->bc),changed
3rd:50%
>>> pow(19,36,41)
25
@in ab:(25-19)/(36-19)=35.2%
@in ac:(25-19)/(41-19)=27.27%
(bc->ab),changed
>>> pow(19,37,41)
24
@in ab:(24-19)/(37-19)=27.7%
@in ac:(24-19)/(41-19)=22.72%
(ab->ab)
>>> pow(19,38,41)
5
@out a, @in ab:(19-5)/(38-5)=42.42%
@in ac:---%
(out:ignored)
>>> pow(19,39,41)
13
@out a, @in ab:(19-13)/(39-13)=23.07%
@in ac:---%
(out:ignored)
>>> pow(19,40,41)
1
@out a, @in ab:(19-1)/(40-1)=46.1%
@in ac:---%
(out:ignored)
>>> pow(19,41,41)
19
@a, in ab:0%
@in ac:0%
(ab->ab)

[8]pow(5,c(5:11),11)*1
pow(5,n,11)poscomment
>>> pow(5,5,11)
1
@out a, @out ab:(5-1)/(5-1)=100%
@in ac:---%
(out:ignored)
>>> pow(5,6,11)
5
@a, @in ab:0%
@in ac:0%
(ab->?)
>>> pow(5,7,11)
3
@out a, @out ab:(5-3)/(7-3)=50%
@in ac:---%
(out:ignored)
50%
>>> pow(5,8,11)
4
@out a, @out ab:(5-4)/(8-4)=25%
@in ac:---%
(out:ignored)
>>> pow(5,9,11)
9
@b, @in ab:100%, @in bc:0%
@in ac:(9-5)/(11-5)=66.66%
(ab->bc),changed?
(ab->ab)
>>> pow(5,10,11)
1
@out a, @out ab:(5-1)/(10-1)=44.44%
@in ac:---%
(out:ignored)
>>> pow(5,11,11)
5
@a, @in ab:0%
@in ac:0%
(bc->ab),changed?
(ab->ab)
1st-pass : check c(50%, near(50%)) in !(out), sel=(5,9,11),66.66%,
_____________@diff(66.66.vs.50%)=16.66%>10%:(out of target)?
2nd-pass : check c(50%, near(50%)) in (out), sel=(5,7,11),50%, is nearest(1st,2nd-pass).

[9]pow(5,c(5:11),11)*2=pow(10,c(10:22),22)
pow(10,n,22)poscomment
>>> pow(10,10,22)
12
@in bc:(12-10)/(22-10)=16.6%
@in ac:(12-10)/(22-10)=16.66%
(bc->?)
>>> pow(10,11,22)
10
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(10,12,22)
12
@b, @in ab:100%, @in bc:0%
@in ac:(12-10)/(22-10)=16.66%
(ab->bc),changed?
(ab->ab)
>>> pow(10,13,22)
10
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
(ab->ab)
>>> pow(10,14,22)
12
pow(5,7,11)*2
@in ab:(12-10)/(14-10)=50%
@in ac:(12-10)/(22-10)=16.66%
(ab->ab)
50%
>>> pow(10,15,22)
10
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(10,16,22)
12
pow(5,8,11)*2
@in ab:(12-10)/(16-10)=33.3%
@in ac:(12-10)/(22-10)=16.66%
(ab->ab)
>>> pow(10,17,22)
10
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(10,18,22)
12
@in ab:(12-10)/(18-10)=25%
@in ac:(12-10)/(22-10)=16.66%
(ab->ab)
>>> pow(10,19,22)
10
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(10,20,22)
12
@in ab:(12-10)/(20-10)=20%
@in ac:(12-10)/(22-10)=16.66%
(ab->ab)
>>> pow(10,21,22)
10
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(10,22,22)
12
@in ab:(12-10)/(22-10)=16.6%
@in ac:(12-10)/(22-10)=16.66%
(ab->ab)
1st-pass : check c(50%, near(50%)) in !(out), sel=none.
2nd-pass : check c(50%, near(50%)) in (out), sel=(b=14=2*7, diff=0%), so sel=pow(5,7,11)*2.

[10]pow(5,c(5:11),11)*3=pow(15,c(15:33),33)
pow(15,n,33)poscomment
>>> pow(15,15,33)
12
@out a, @out ab:(15-12)/(15-12)=100%
@in ac:---%
(out:ignored)
>>> pow(15,16,33)
15
@a, @in ab:0%
@in ac:0%
(ab->?)
>>> pow(15,17,33)
27
@in bc:(27-17)/(33-17)=62.5%
@in ac:(27-15)/(33-15)=66.66%
(ab->bc),changed
>>> pow(15,18,33)
9
@out a, @out ab:(15-9)/(18-9)=66.6%
@in ac:---%
(out:ignored)
>>> pow(15,19,33)
3
@out a, @out ab:(15-3)/(19-3)=75%
@in ac:---%
(out:ignored)
>>> pow(15,20,33)
12
@out a, @out ab:(15-12)/(20-12)=37.5%
@in ac:---%
(out:ignored)
>>> pow(15,21,33)
15
pow(5,7,11)*3
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(15,22,33)
27
pow(5.7.33,11)*3
@in bc:(27-22)/(33-22)=45.45%
@in ac:(27-15)/(33-15)=66.66%
(ab->bc),changed
@diff(45.45.vs.50)=4.55%
>>> pow(15,23,33)
9
pow(5,7.66,11)*3
@out a, @out ab:(15-9)/(23-9)=42.8%
@in ac:---%
(out:ignored)
@diff(42.8.vs.50)=7.2%
>>> pow(15,24,33)
3
pow(5,8,11)*3
@out a, @out ab:(15-3)/(24-3)=57.1%
@in ac:---%
(out:ignored)
@diff(57.1.vs.50)=7.1%
>>> pow(15,25,33)
12
@out a, @out ab:(15-12)/(25-12)=23.0%
@in ac:---%
(out:ignored)
>>> pow(15,26,33)
15
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(15,27,33)
27
@b, @in ab:100%, @in bc:0%
@in ac:(27-15)/(33-15)=66.66%
(ab->bc),changed
(ab->ab)
>>> pow(15,28,33)
9
@out a, @out ab:(15-9)/(28-9)=31.57%
@in ac:---%
(out:ignored)
>>> pow(15,29,33)
3
pow(5,9.66,11)*3
@out a, @out ab:(15-3)/(29-3)=46.1%
@in ac:---%
(out:ignored)
@diff(46.1.vs.50)=3.84
>>> pow(15,30,33)
12
@out a, @out ab:(15-12)/(30-12)=16.67%
@in ac:---%
(out:ignored)
>>> pow(15,31,33)
15
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
(ab->ab)
>>> pow(15,32,33)
27
@in ab:(27-15)/(32-15)=70.5%
@in ac:(27-15)/(33-15)=66.66%
(ab->ab)
>>> pow(15,33,33)
9
@out a, @out ab:(15-9)/(33-9)=25%
@in ac:---%
(out:ignored)
1st-pass : check c(50%, near(50%)) in !(out),
___sel=(b=22=3*7.33, diff=4.5%)
2nd-pass : check c(50%, near(50%)) in (out),
___sel=((b=23=3*7.66, diff=7.2%),
_______(b=24=3*8, diff=7.1%),
_______(b=29=3*9.66, diff=3.84%)),
@ b=just int()=3*8, pow(5,8,11)*3.

[11]pow(2,c(2:22),22)
pow(2,n,22)poscomment
>>> pow(2,2,22)
4
@in bc:(4-2)/(22-2)=10%
@in ac:(4-2)/(22-2)=10%
(bc->?)
>>> pow(2,3,22)
8
@in bc:(8-3)/(22-3)=26.3%
@in ac:(8-2)/(22-2)=30%
(bc->bc)
>>> pow(2,4,22)
16
pow(1,2,22)*2
@in bc:(16-4)/(22-4)=66.6%
@in ac:(16-2)/(22-2)=70%
(bc->bc)
@diff(66.6.vs.50)=16.6>10%
>>> pow(2,5,22)
10
pow(1,2.5,11)*2
@in bc:(10-5)/(22-5)=29.4%
@in ac:(10-2)/(22-2)=40%
(bc->bc)
@diff(40.vs.50)=10~10%
>>> pow(2,6,22)
20
@in bc:(20-6)/(22-6)=87.5%
@in ac:(20-2)/(22-2)=90%
(bc->bc)
>>> pow(2,7,22)
18
@in bc:(18-7)/(22-7)=73.3%
@in ac:(18-2)/(22-2)=80%
(bc->bc)
>>> pow(2,8,22)
14
pow(1,4,11)*2
@in bc:(14-8)/(22-8)=42.8%
@in ac:(14-2)/(22-2)=60%
(bc->bc)
@diff(42.8.vs.50)=7.2%
@diff(60.vs.50)=10~10%
>>> pow(2,9,22)
6
pow(1,4.5,11)*2
@in ab:(6-2)/(9-2)=57.1%
@in ac:(6-2)/(22-2)=20%
(bc->ab),changed
@diff(57.1.vs.50)=7.1%
>>> pow(2,10,22)
12
pow(1,5,11)*2
@in bc:(12-10)/(22-10)=16.6%
@in ac:(12-2)/(22-2)=50%
(ab->bc),changed
1st:50%
>>> pow(2,11,22)
2
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(2,12,22)
4
@in ab:(4-2)/(12-2)=20%
@in ac:(4-2)/(22-2)=10%
(ab->ab)
>>> pow(2,13,22)
8
pow(1,6.5,11)*2
@in ab:(8-2)/(13-2)=54.5%
@in ac:(8-2)/(22-2)=30%
(ab->ab)
@diff(54.5.vs.50)=4.5%
>>> pow(2,14,22)
16
@in bc:(16-14)/(22-14)=25%
@in ac:(16-2)/(22-2)=70%
(ab->bc),changed
>>> pow(2,15,22)
10
@in ab:(10-2)/(15-2)=61.5%
@in ac:(10-2)/(22-2)=40%
(bc->ab),changed
@diff(61.5.vs.50)=11.5>10%
@diff(40.vs.50)=10~10%
>>> pow(2,16,22)
20
pow(1,8,11)*2
@in bc:(20-16)/(22-16)=66.6%
@in ac:(20-2)/(22-2)=90%
(ab->bc),changed
@diff(66.6.vs.50)=16.6>10%
>>> pow(2,17,22)
18
@in bc:(18-17)/(22-17)=20%
@in ac:(18-2)/(22-2)=80%
(bc->bc)
>>> pow(2,18,22)
14
pow(1,9,11)*2
@in ab:(14-2)/(18-2)=75%
@in ac:(14-2)/(22-2)=60%
(bc->ab),changed
@diff(60.vs.50)=10~10%
>>> pow(2,19,22)
6
@in ab:(6-2)/(19-2)=23.5%
@in ac:(6-2)/(22-2)=20%
(ab->ab)
>>> pow(2,20,22)
12
pow(1,10,11)*2
@in ab:(12-2)/(20-2)=55.5%
@in ac:(12-2)/(22-2)=50%
(ab->ab)
@diff(55.5.vs.50)=5.5%
2nd:50%
>>> pow(2,21,22)
2
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(2,22,22)
4
@in ab:(4-2)/(22-2)=10%
@in ac:(4-2)/(22-2)=10%
(ab->ab)
1st-pass : check c(50%, near(50%)) in !(out), sel=none
2nd-pass : check c(50%, near(50%)) in (out), sel=(1,5,11)*2, 1st:50%,
________________________________________with (b=just int, c(ab,bc)=changed);

[12]pow(3,c(3:33),33)
pow(3,n,33)poscomment
>>> pow(3,3,33)
27
@in bc:(27-3)/(33-3)=80% (bc->?)
>>> pow(3,4,33)
15
pow(1,1.33,11)*3
@in bc:(15-4)/(33-4)=37.9%
@in ac:(15-3)/(33-3)=40%
(bc->bc)
@diff(40.vs.50)=10~10%
>>> pow(3,5,33)
12
@in bc:(12-5)/(33-5)=25%
@in ac:(12-3)/(33-3)=30%
(bc->bc)
>>> pow(3,6,33)
3
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(3,7,33)
9
@in bc:(9-7)/(33-7)=7.69%
@in ac:(9-3)/(33-3)=20%
(ab->bc),changed
>>> pow(3,8,33)
27
@in bc:(27-8)/(33-8)=76%
@in ac:(27-3)/(33-3)=80%
(bc->bc)
>>> pow(3,9,33)
15
pow(1,3,11)*3
@in bc:(15-9)/(33-9)=25%
@in ac:(15-3)/(33-3)=40%
(bc->bc)
@diff(40.vs.50)=10~10%
>>> pow(3,10,33)
12
@in bc:(12-10)/(33-10)=8.69%
@in ac:(12-3)/(33-3)=30%
(bc->bc)
>>> pow(3,11,33)
3
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(3,12,33)
9
@in ab:(9-3)/(12-3)=66.6%
@in ac:(9-3)/(33-3)=20%
(ab->ab)
@diff(66.6.vs.50)=16.6>10%
>>> pow(3,13,33)
27
@in bc:(27-13)/(33-13)=70%
@in ac:(27-3)/(33-3)=80%
(ab->bc),changed
>>> pow(3,14,33)
15
pow(1,4.66,11)*3
@in bc:(15-14)/(33-14)=5.2%
@in ac:(15-3)/(33-3)=40%
(bc->bc)
@diff(40.vs.50)=10~10%
>>> pow(3,15,33)
12
pow(1,5,11)*3
@in ab:(12-3)/(15-3)=75%
@in ac:(12-3)/(33-3)=30%
(bc->ab),changed
>>> pow(3,16,33)
3
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(3,17,33)
9
pow(1,5.66,11)*3
@in ab:(9-3)/(17-3)=42.8%
@in ac:(9-3)/(33-3)=20%
(ab->ab)
@diff(42.8.vs.50)=7.2
>>> pow(3,18,33)
27
@in bc:(27-18)/(33-18)=60%
@in ac:(27-3)/(33-3)=80%
(ab->bc),changed
>>> pow(3,19,33)
15
pow(1,6.33,11)*3
@in ab:(15-3)/(19-3)=75%
@in ac:(15-3)/(33-3)=40%
(bc->ab),changed
@diff(40.vs.50)=10~10%
>>> pow(3,20,33)
12
pow(1,6.66,11)*3
@in ab:(12-3)/(20-3)=52.9%
@in ac:(12-3)/(33-3)=30%
(ab->ab)
@diff(52.9.vs.50)=2.9%
>>> pow(3,21,33)
3
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(3,22,33)
9
@in ab:(9-3)/(22-3)=31.5%
@in ac:(9-3)/(33-3)=20%
(ab->ab)
>>> pow(3,23,33)
27
pow(1,7.66,11)*3
@in bc:(27-23)/(33-23)=40%
@in ac:(27-3)/(33-3)=80%
(ab->bc),changed
@diff(40.vs.50)=10~10%
>>> pow(3,24,33)
15
pow(1,8,11)*3
@in ab:(15-3)/(24-3)=57.1%
@in ac:(15-3)/(33-3)=40%
(bc->ab),changed
@diff(57.1.vs.50)=7.1%
@diff(40.vs.50)=10~10%
>>> pow(3,25,33)
12
pow(1,8.33,11)*3
@in ab:(12-3)/(25-3)=40.9%
@in ac:(12-3)/(33-3)=30%
(ab->ab)
@diff(40.9.vs.50)=9.1%
>>> pow(3,26,33)
3
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(3,27,33)
9
@in ab:(9-3)/(27-3)=25%
@in ac:(9-3)/(33-3)=20%
(ab->ab)
>>> pow(3,28,33)
27
@in ab:(27-3)/(28-3)=96%
@in ac:(27-3)/(33-3)=80%
(ab->ab)
>>> pow(3,29,33)
15
pow(1,9.66,11)*3
@in ab:(15-3)/(29-3)=46.1%
@in ac:(15-3)/(33-3)=40%
(ab->ab)
@diff(46.1.vs.50)=3.9%
@diif(40.vs.50)=10~10%
>>> pow(3,30,33)
12
@in ab:(12-3)/(30-3)=33.3%
@in ac:(12-3)/(33-3)=30%
(ab->ab)
>>> pow(3,31,33)
3
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(3,32,33)
9
@in ab:(9-3)/(32-3)=20.68%
@in ac:(9-3)/(33-3)=20%
(ab->ab)
>>> pow(3,33,33)
27
@in ab:(27-3)/(33-3)=80%
@in ac:(27-3)/(33-3)=80%
(ab->ab)
1st-pass : check c(50%, near(50%)) in !(out), sel=none
2nd-pass : check c(50%, near(50%)) in (out), sel=(1,8,11)*3,
____________1st:near(50%) with c(abs(diff)<10%, b=just int, c(ab,bc)=changed);

[13]pow(4,c(4:44),44)
pow(4,n,44)poscomment
>>> pow(4,4,44)
36
@in bc:(36-4)/(44-4)=80%
@in ac:(36-4)/(44-4)=80%
(bc->?)
>>> pow(4,5,44)
12
@in bc:(12-5)/(44-5)=17.9%
@in ac:(12-4)/(44-4)=20%
(bc->bc)
>>> pow(4,6,44)
4
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(4,7,44)
16
@in bc:(16-7)/(44-7)=24.3%
@in ac:(16-4)/(44-4)=30%
(ab->bc),changed
>>> pow(4,8,44)
20
pow(1,2,11)*4
@in bc:(20-8)/(44-8)=33.3%
@in ac:(20-4)/(44-4)=40%
(bc->bc)
@diff(40.vs.50)=10~10%
>>> pow(4,9,44)
36
@in bc:(36-9)/(44-9)=77.1%
@in ac:(36-4)/(44-4)=80%
(bc->bc)
>>> pow(4,10,44)
12
@in bc:(12-10)/(44-10)=5.8%
@in ac:(12-4)/(44-4)=20%
(bc->bc)
>>> pow(4,11,44)
4
@a, @in ab:0%
@in ac:0%
(bc->ab),changed
>>> pow(4,12,44)
16
@in bc:(16-12)/(44-12)=12.5%
@in ac:(16-4)/(44-4)=30%
(ab->bc),changed
>>> pow(4,13,44)
20
pow(1,3.25,11)*4
@in bc:(20-13)/(44-13)=22.5%
@in ac:(20-4)/(44-4)=40%
(bc->bc)
@diff(40.vs.50)=10~10%
>>> pow(4,14,44)
36
@in bc:(36-14)/(44-14)=73.3%
@in ac:(36-4)/(44-4)=80%
(bc->bc)
>>> pow(4,15,44)
12
@in ab:(12-4)/(15-4)=72.7%
@in ac:(12-4)/(44-4)=20%
(bc->ab),changed
>>> pow(4,16,44)
4
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(4,17,44)
16
@in ab:(16-4)/(17-4)=92.3%
@in ac:(16-4)/(44-4)=30%
(ab->ab)
>>> pow(4,18,44)
20
pow(1,4.5,11)*4
@in bc:(20-18)/(44-18)=7.6%
@in ac:(20-4)/(44-4)=40%
(ab->bc),changed
@diff(40.vs.50)=10~10%
>>> pow(4,19,44)
36
pow(1,4.75,11)*4
@in bc:(36-19)/(44-19)=68%
@in ac:(36-4)/(44-4)=80%
(bc->bc)
@diff(68.vs.50)=18>10%
>>> pow(4,20,44)
12
pow(1,5,11)*4
@in ab:(12-4)/(20-4)=50%
@in ac:(12-4)/(44-4)=20%
(bc->ab),changed
1st:50%
>>> pow(4,21,44)
4
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(4,22,44)
16
pow(1,5.5,11)*4
@in ab:(16-4)/(22-4)=66.6%
@in ac:(16-4)/(44-4)=30%
(ab->ab)
@diff(66.6.vs.50)=16.6>10%
>>> pow(4,23,44)
20
pow(1,5.75,11)*4
@in ab:(20-4)/(23-4)=84.2%
@in ac:(20-4)/(44-4)=40%
(ab->ab)
@diff(40.vs.50)=10~10%
>>> pow(4,24,44)
36
pow(1,6,11)*4
@in bc:(36-24)/(44-24)=60%
@in ac:(36-4)/(44-4)=80%
(ab->bc),changed
@diff(60.vs.50)=10~10%
>>> pow(4,25,44)
12
@in ab:(12-4)/(25-4)=38%
@in ac:(12-4)/(44-4)=20%
(bc->ab),changed
>>> pow(4,26,44)
4
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(4,27,44)
16
pow(1,6.75,11)*4
@in ab:(16-4)/(27-4)=52.1%
@in ac:(16-4)/(44-4)=30%
(ab->ab)
@diff(52.1.vs.50)=2.1%
>>> pow(4,28,44)
20
pow(1,7,11)*4
@in ab:(20-4)/(28-4)=66.6%
@in ac:(20-4)/(44-4)=40%
(ab->ab)
@diff(66.6.vs.50)=16.6>10%
@diff(40.vs.50)=10~10%
>>> pow(4,29,44)
36
pow(1,7.25,11)*4
@in bc:(36-29)/(44-29)=46.6%
@in ac:(36-4)/(44-4)=80%
(ab->bc),changed
@diff(46.6.vs.50)=3.4
>>> pow(4,30,44)
12
@in ab:(12-4)/(30-4)=30.7%
@in ac:(12-4)/(44-4)=20%
(bc->ab),changed
>>> pow(4,31,44)
4
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(4,32,44)
16
pow(1,8,11)*4
@in ab:(16-4)/(32-4)=42.8%
@in ac:(16-4)(44-4)=30%
(ab->ab)
@diff(42.8.vs.50)=7.2%
>>> pow(4,33,44)
20
pow(1,8.25,11)*4
@in ab:(20-4)/(33-4)=55.17%
@in ac:(20-4)/(44-4)=40%
(ab->ab)
@diff(55.17.vs.50)=5.17
@diff(40.vs.50)=10~10%
>>> pow(4,34,44)
36
@in bc:(36-34)/(44-34)=20%
@in ac:(36-4)/(44-4)=80%
(ab->bc),changed
>>> pow(4,35,44)
12
@in ab:(12-4)/(35-4)=25.8%
@in ac:(12-4)/(44-4)=20%
(bc->ab),changed
>>> pow(4,36,44)
4
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(4,37,44)
16
@in ab:(16-4)/(37-4)=36.3%
@in ac:(16-4)/(44-4)=30%
(ab->ab)
>>> pow(4,38,44)
20
pow(1,9.5,11)*4
@in ab:(20-4)/(38-4)=47.0%
@in ac:(20-4)/(44-4)=40%
(ab->ab)
@diff(47.vs.50)=3
@diff(40.vs.50)=10~10%
>>> pow(4,39,44)
36
@in ab:(36-4)/(39-4)=91.4%
@in ac:(36-4)/(44-4)=80%
(ab->ab)
>>> pow(4,40,44)
12
@in ab:(12-4)/(40-4)=22.2%
@in ac:(12-4)/(44-4)=20%
(ab->ab)
>>> pow(4,41,44)
4
@a, @in ab:0%
@in ac:0%
(ab->ab)
>>> pow(4,42,44)
16
@in ab:(16-4)/(42-4)=31.5%
@in ac:(16-4)/(44-4)=30%
(ab->ab)
>>> pow(4,43,44)
20
pow(1,10.75,11)*4
@in ab:(20-4)/(43-4)=41.0%
@in ac:(20-4)/(44-4)=40%
(ab->ab)
@diff(41.vs.50)=9
@diff(40.vs.50)=10~10%
>>> pow(4,44,44)
36
@in ab:(36-4)/(44-4)=80%
@in ac:(36-4)/(44-4)=80%
(ab->ab)
1st-pass : check c(50%, near(50%)) in !(out), sel=none
2nd-pass : check c(50%, near(50%)) in (out), sel=(1,5,11)*4, 1st:50%,
__________________with c(abs(diff)<10%, b=just int, c(ab,bc)=changed);
@@@
borderには、選択されるべき理由があった?
Was there a reason why border should be chosen?
end.

2022年12月23日金曜日

Garbage? : past logged (for prime num)...

@順不同.
[1]素数判定に、60進数を利用できるか? @sqrt()の60進数展開...(2015)
[2]...c(4n+1,4n+3)の分類...(2015)
[3]4n+1素数,sqrt()の連分数傾向(2014)
[4]60進数展開の少数部上位3桁から : c(min=L, median=M, max=H)...(2015)
___c(L,M,H)の組み合わせから、比率を作る。rate1=(HL)/M^2, rate2=M^2/(HL)
___c(rate1,rate2)の傾向から、、、@@@

[5]「音楽と数学」、音階から何か知見?(2015)
[6]遺伝子暗号から、何か知見?(2015)
[7]パルマー系列、水素スペクトル系列から、何か知見?(2014), @リュードベリ定数は関連ありか?

@@@{dupの傾向を知れば、一歩ゴールに近づくかと...}:かなり時間を割いている...
[8]large(diff, ?)から、dupの境界値を導出するには?(2015)
[9]フィボナッチ数の比率から、dupの境界値を導出するには?(2015)
[9-1]60進数で、平方根の近似値から、dup境界値を得る?(2015)
@@@
[10]4n+1素数(org)から、先行する4n+1素数をすべて生成できるか?(2014)
__例)5から始めて、すべての(4n+1)素数を順次生成していけるか...

[11]盛んに、dup()が出てくるが、思い出さない。。。?!
__[a](4n+1)素数から、選考する(4n+1)素数を生成する流れでした。(2014)
__[b]例)cal : x-2*sqrt(x)-A=0, A=1193, x=?
org
(4n+1)
back
(4n+1)
cal
A=org,x=?
fore
(4n+1)
comment sqrt(fore)diff(now.vs.prev)
sqrt(fore)
11931249x≈1264.112771277 as dup35.735aaa
12011249x≈1272.31277same
12131277x≈1284.712891289 as dup35.9020.167
=35.902-35.735
12171277x≈1288.81289same
@やはり、(wolframalpha)は楽しい。以前は、手計算・関数電卓、excel(ods)などでやっていたのに...(now:2022)

[12]dupの傾向を調べる。(2014)
__[a]dupの個数の変化を見る。c(u, d, sa)=c(up:増加, down:減少, same:変化なし).
__[b]sqrt(dup)の整数部を基準に、同一内のdup個数の増減傾向を見た...が...:廃棄。

@@@@
end.

Garbage? : drown in the sea of ​​primes...

[1]素数から年内に離れるつもりが、まだやっています。
[2]c(50:100)の素数に関して、フラットな数字群ではなく、グループ化?クラスタリング化?できるか見たかった。
[3](wolframalpha)で、以下の2式に素数を代入して、結果との関係を見た。
__x-2*sqrt(x)-A=0, A=53, x=? : x ≈ 69.697
__x-2*sqrt(x)-A=0, A=?, x=53 : A≈38.4398

[4]別プロジェクトの経過メモ)
__[a]中断しているn=8(@fc=started)は、(@fc=x)とすると終わってしまうので、開始の可能性として、c(@f,@c)のいずれもあり得るとして、結果の偏りがない方を選択する方向でまとめる予定であるが、また、n=8と小さい値なので、段数は3段となり、先頭で判断できずにスキップすると、その先の判断の可能性が狭まってしまうので、候補としてはあげるが、選考対象外となるなど。@htmlの編集は繁雑すぎた。思考がとぎれます。
__[b]n=c(1:100)で、式1、式2を見て、素数のavg()を見てみると、なかなか感触がよかった。まとめにモチベーションが低下すると、年内終結の期限に時間切れで閉じることに?

[5]n=1009で試行。現時点の結論は、topイメージのコメント欄にある通り。
@画面の分割貼り付けで、恐縮です。
n=1009-top.(0)
[5-1]n=1009に関しては、center=11個目であるが、そのcenterをずらしたら、何がみえるか?@以下、center=c(5,9,10,15)と試行したもの。
n=1009.(1)
[5-2]どこを切っても、金太郎あめ的な、景色が見える。@日本的な表現ですが。
__やはり、式の意味は、素数の分布が、その前後のどこくらいの範囲で散らばっているかを
式1、式2が、当面仮に示していると感じられる...
n=1009.(2)
[5-3]blank.
n=1009.(3)
[5-4]n=971も試行。
n=971.
[5-5]上記を実行する前段階として、n=c(1:100)の素数について、式1、式2のavgを検討していた。まとめは未完であるが、その一部を抜粋!
n=71.to.97 (as example)
[6]来年(2023)は、良い年でありますように!
@@@
end.

2022年12月3日土曜日

Garbage? : idea of border : init=5, init(@c>f=c)=>all(@c>f=c)?, (v12/5,6,7,8-11,13-18,26,27)

[1]init=5,init(@c>f)=all(@c>f)を見てみる。
[2]init=5, expected_border=c(5,7,8,11).
[3]border_target, n=c(6:10, 10 < p < 50); p=c(11,13,17,19,23,29,41,43,47);

[4]探索条件は以下。
__[a]nから逆にたどり、init=5に至るパスをすべて確認する。
_____矢印の向きは無関係で、つながっていれば、リンク可能とする。
________c(src->n, n->dist)は、c(src--n, dist--n)として扱う。
_____探索するリンクは、n以下とする。

__[b]5に至れば、同一レベルの他の検索を止める。Loopするため。

__[c]検索が重複しないように、共通パスのみ探索する。(tryout)
__[c]共通パスの扱いを変更。
____[c-1] handling as c(org,tryout) : 検索が重複しないように、共通パスのみ探索する。
______共通パスの参照先は、パスの分岐の少ない方を基準にする。c(7,8)は見直しで、共通パスは1件のみとする。

____[c-2] handling as c(tryout2) : スキップしていた共通パスを除外する方針を止めて、共通パスもsame先の[fc status]で扱う。これは、最後に残留していたn=23のため。@fc=stopped以外は生かす。nが大きくなると、共通パスが増加し、その存在を無視することはどうなのかと思う。
____[c-2] handling as c(tryout2) : Stop the policy of excluding the common path that was skipped, and handle the common path with the same destination [fc status]. This is because n=23 remained at the end. Use anything other than @fc=stopped. As n grows, the common paths increase, and I wonder what it's like to ignore their existence. (by google-translation)

____[c-3]tryout2作業終了後、n=c(7,8)がborder(init=5)の対象から外れた。共通パスの扱いで、@fc-statusを安易にコピーしたのが誤りか? そのために、共通パスでも、initまで探索し、その経路での@fc-statusで判断する。これをfull-path処理とする。
____[c-3]After the work of tryout2, n=c(7,8) was removed from border(init=5). Is it an error to easily copy @fc-status when handling a common path? For that reason, even if it is a common path, search up to init and judge by @fc-status on that route. This is called full-path processing.

__[d]パスのリンクの途中/or/終端に、(@fc)があれば、探索中止とする。パスの先頭状態の条件についても、別枠ではなく、ここで言及した。
____[d-1]パスの先頭で、c(@f,@c)のいずれかが =0の場合、いずれかに偏っているため、先頭をスキップして、次段からc(@f,@c)を評価する。
______n=c(23,29)が該当している。
____[d-1]If any of c(@f,@c) is =0 at the beginning of the path, skip the beginning and evaluate c(@f,@c) from the next stage .
____[d-2]10%ルールがここでも現れた。n=19が該当。偏った一方が10%以下ならば、[d-1]と同様に、次段から処理する。
___________n=19の次段は、単一ではなく、複数(19-10-*, 19-11-*, 19-13-*)なので、結果を多数決で判定する。
____[d-3]最終表のfc-statusで、結果が偏っているものは、n=9がある。あくまでも先頭パスのバランスなので、見ると、@c=c(invalid, @fc=stopped)なので、@cの割合として使えないと判断した場合、path=9-4-*の単一で、@f*に偏っているとみなす。n=4に関して見てみる。
_________[n=4]result()=c(@f = @c, @f > @c)から、(init=5のグループ)から[n=9]を除外する。

__[e]探索パスで、見るべきc(@f,@c)は、パスの始めと終わりとする。
______最終的にc(@f,@c)をカウントして、init=5の場合、(c > f, @f < @c)が、borderの構成員であることを導きたい。
____[e-1] handling as c(org,tryout2) : パスの始めと終わりとする。
____[e-2] handling as c(tryout) : パスの先頭から最後までの全分岐のc(@f,@c)をカウントして、多数決で、そのパスのwhich=c(@f,@c)を決定する。 n=c(19,23)で、試行した。

__[f]initのc(@f,@c)に関しては、以下の条件で求めることにする。
____[f.1]Not(=!) used [option]=c(A.eq.2.5, A.eq.0.7, A.eq.0.8).
____[f.2]c(src->init, init->dist)の、c(src, dist)の絞り込み条件は以下。
____________@矢印の向きは問わないので、=c(src--init, dist--init)として扱う。
__________if (p < init) existed, apply(p < init).
__________if (p < init) !existed, apply(all(p)).
__________if all(p) !existed, apply(all).


__[g]Limit the depth of a path : within int(sqrt(init + n)); @as depth-limiter;
____深さは、c(init,n)に比例する。例:c(init=11,n=19,depth=5), c(init=5,n=19,depth=4),...
____Depth is proportional to c(init,n). Example: c(init=11,n=19,depth=5), c(init=5,n=19,depth=4),...

__[h]パスの先頭に@fcがある場合、今回は、n=8が該当する。
____fullpath : @f > @c;で、init=5のborder()から外れる。これを回避するための検討です。
____先頭@fcの扱いは、以下を考えた。
____{1}今まで通り、(@fc)=xで、相殺(先頭を除外)。その次から評価する。
________result=(x*5, f*1, c*0); @f > @c; =!expected.; (c=0):偏りあり。除外。
________@やはり、今回3段なので、先頭を除外すると2段になり、判断は難しいのでは?
_______1c-f@cf=x
2fc-f-c@fc@fc=x
3fc-f-c@fc@fc=x
4fc-f-c@fc@fc=x
5fc-f-f(@fc,f*2)=f
6fc-c-f(@fc,@cf*1)=x
7out---
8out---
____{2}相殺ではないが、先頭--次段で、同一(@f,@c)をペアとして、消去する。残留したもので評価する。
_______result=(x*2, f*1, c*3); @f < @c; =expected; (?*0)がないので、偏りなし。採用!?
_______@今まで、相殺は@fcで、ペアの考えはなかった。違和感あるが。
_______1c-f@cf=x
2(fc-f)-c,=>(c)-c@cc=c
3(fc-f)-c,=>(c)-c@cc=c
4(fc-f)-c,=>(c)-c@cc=c
5(fc-f)-f,=>(c)-f@cf=x
6(fc-c)-f,=>(f)-f@ff=f
7out---
8out---
____{3}c(@f,@c)のいずれにもなれるとして、結果に偏りがない方を選択する。
______{3-1:@fc=fの場合}, result=(x*1, f*5, c*0); @f > @c; =!expected; (c=0):偏りあり。除外。
_______1c-f@cf=x
2fc-f-c,=>f-f-c(f*2,c*1)=f
3fc-f-c,=>f-f-c(f*2,c*1)=f
4fc-f-c,=>f-f-c(f*2,c*1)=f
5fc-f-f,=>f-f-f(f*3,c*0)=f
6fc-c-f,=>f-c-f(f*2,c*1)=f
7out---
8out---

______{3-2:@fc=cの場合}, result=(x*1, f*1, c*4); @f < @c; =expected; (f*1,=1/5=20%)なので、偏りなし。採用!?
_______1c-f@cf=x
2fc-f-c,=>c-f-c(f*1,c*2)=c
3fc-f-c,=>c-f-c(f*1,c*2)=c
4fc-f-c,=>c-f-c(f*1,c*2)=c
5fc-f-f,=>c-f-f(f*2,c*1)=f
6fc-c-f,=>c-c-f(f*1,c*2)=c
7out---
8out---

____{4}偏りの考えは、先の[d-2,d-3]と同じ流れなので、採用しやすい。よって、上記の{3}を採用する。

__[i]長期間編集しているので、整合性が崩れていると思われる。ここで仕切り直しで、各nの頭にあるresultの説明を再度まとめる。
____@初期に編集したものは、以下の順番で、歯抜けになっているかもしれないので、再チェック要!:12/27:done.
____result(対象No., !(対象外のNo.)).

____result(1) : 除外=c(!pair=invalid, @fc=stopped, search=stopped, looped),パスの先頭と終端の組み合わせで判定。
____result(1-1) : tryout : 除外=c(same), (See [e-2]), パスの全(@f,@c)を見て、多数決で判定する。
____result(1-2) : depth-limiter : 除外=c(same), パスの深さで、対象を選別する。パスの先頭と終端判定(like result(1))。

____result(2) : tryout2 : 除外=c(!pair=invalid, @fc=stopped, search=stopped, looped), パスの先頭と終端判定(like result(1))。
______@(search=stopped)を除外しないが、使用する@fcは、(same No.)のものを使う。
____result(2-1) : tryout2,depth-limiter : 除外=c(same), result(2)のdepth-limitter版。
____result(2-2) : tryout2,tryout : 除外=c(same), result(2)のtryout版。
____result(2-3) : tryout2,tryout,depth-limitter : 除外=c(same), result(2)の(tryout,depth-limiter)版。

____result(3) : fullpath : included=c(tryout,depth-limiter) : 除外=c(!pair=invalid, @fc=stopped, search=stopped, looped), パスの全(@f,@c)を見る。
______@(search=stopped)を除外しないが、使用する@fcは、(same No.)のではなく、自分自身のものを使う。

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[n=5]: (p < init) : result(8,9)=c(f*1, c*1), @f = @c; @expected : @f < @c;
_____(all < init) : result(1:4,7,8,9)=c(@f*3, @c*4), @f < @c; @selected this!
*__depth-limiter=int(sqrt(init+n=5+5=10))=3;
*____(in),depth(path) < depth-limiter : result(1:4,7,8,9)=same, @f < @c;
#__tryout2 : result=same, @f < @c;
#__fullpath(tryout2; tryout,out) : result=same, @f < @c;
No.path(n to init)fc
status
commentdepth
(path)
depth(path)
.vs.limiter
10.1--5@c@c!p2in
20.2--5@c@c!p2in
30.5--5@c@c!p2in
40.6--5@f@f!p2in
50.7--5@f@f!p,!used in [option].2in
60.8--5@f@f!p,!used in [option].2in
71--5@f@f!p2in
82--5@f@fp < init,2in
93--5@c@cp < init,2in
109--5@c@c!p > init,2in
1110--5@f@f!p > init,2in
1211--5@f@fp > init,2in

[n=6]: (?<6) :result(1:4)=c(cf,cf,ff,cc)=(cf*2=ignored, ff=f*1, cc=c*1), @f = @c;
___common:none;
*__depth-limiter=int(sqrt(init+n=11))=3;
*____(in),depth(path) < depth-limiter : result(1:4)=same, @f = @c;
#__tryout2 : result=same, @f = @c;
__fullpath() : result=same, @f = @c;
No.path(n to init)fc
status
common
path
depth
(path)
depth(path)
.vs.limiter
16@c--0.6--5@f@cf?2in
26@c--1--5@f@cf?2in
36@f--2--5@f@ff?2in
46@c--3--5@c@cc?2in

[n=7]: (?<7) :result(1:6, !(7))=c((fc=cf)*2, ff=f*1, cc=c*3), @f < @c;
___common:result(1:6,out=7)=c((fc=cf)*2, ff=f*1, cc=c*3), @f < @c;
___common:result(2:7,out=1)=c((cf=fc)*3, f*0, cc=c*3), @f < @c;
___tryout : result(1:6)=c(x*1, f*2, c*3), @f < @c;
*__depth-limiter=int(sqrt(init+n=12))=3;
*____(in),depth(path) < depth-limiter : result()=same, @f < @c;
#__tryout2 : result(1:7)=c((fc=cf)*2, ff=f*2, cc=c*3), @f < @c;
#__tryout2 : with tryout : result(1;7)=c(x*1, f*3, c*3), @f = @c;
___fullpath : result(1:7)=c(x*1, f*2, c*4), @f < @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
17@f--2--5@f
7-f-2-f-5
@ff
(f*2)=f
same as 7-4-2(No.7)2in
27@f--3--5@c
7-f-3-c-5
@fc
(f*1,c*1)=x
?2in
37@c--4--0.1--5@c
7-c-4-f-0.1-c-5
@cc
(f*1,c*2)=c
?3in
47@c--4--0.2--5@c
7-c-4-f-0.2-c-5
@cc
(f*1,c*2)=c
?3in
57@c--4--0.5--5@c
7-c-4-f-0.5-c-5
@cc
(f*1,c*2)=c
?3in
67@c--4--1--5@f
7-c-4-f-1-f-5
@cf
(f*2,c*1)=f
?3in
77@c--4--2
full=7-c-4-c-2-f-5
search=stopped
full=@cf,(f*1,c*2)=c
same as 7-2(No.1),@ff,(f)
full=@cf,(c)
2
3
in
in

[n=8]: (?<8) :result(1:6)=c(cf*1=ignored, (fc,f)=f*2, (fc,c)=c*3), @f < @c;
__result(1:8,!(6,7))=c(cf*1, (fc,f)=f*1, (fc.c)=c*4), @f < @c;
___common:result(1:5,out=6)=c(cf*1, (fc,f)=f*1, (fc,c)=c*3), @f < @c;
___common:result(2:6,out=1)=c(cf*0, (fc,f)=f*2, (fc,c)=c*3), @f < @c;
___tryout : result(1:5)=c(x*4, f*1, c*0), @f > @c; @!expected.
___tryout : result(1:8,!(6,7))=c(x*4, f*1, c*1), @f = @c; @!expected.
*__depth-limiter=int(sqrt(init+n=13))=3;
*____(in),depth(path) < depth-limiter : result(1:8,!(6:8))=c(cf*1, (fc,f)=f*1, (fc,c)=c*3), @f < @c;
#__tryout2 : result(1:8)=c(cf*3, (fc.f)=f*1, (fc,c)=c*4), @f < @c;
#__tryout2 : (in),depth(path) < depth-limiter : result(1:8,!(8))=c(cf*3, (fc,f)=f*1, (fc,c)=c*3), @f < @c;
#__tryout2 : with tryout : result(1:8)=c(x*6, f*1, c*1), @f = @c; @!expected.
#__tryout2 : with tryout : (in),depth(path) < depth-limiter : result(1:8,!(8))=c(x*6, f*1, c*0), @f > @c; @!expected.
__fullpath : result(1:8, !(out=c(7,8))=c(x*5, f*1, c*0), @f > @c; @!expected.

No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
18@c--2--5@f
8-c-2-f-5
@cf
(f*1,c*1)=x
same as 8-4(No.6)2in
28@fc--4--0.1--5@c
8-fc-4-f-0.1-c-5
@fc,c
(fc*1=x,f*1,c*1)=x
?3in
38@fc--4--0.2--5@c
8-fc-4-f-0.2-c-5
@fc,c
(fc*1,f*1,c*1)=x
?3in
48@fc--4--0.5--5@c
8-fc-4-f-0.5-c-5
@fc,c
(fc*1,f*1,c*1)=x
?3in
58@fc--4--1--5@f
8-fc-4-f-1-f-5
@fc,f
(fc*1,f*2,c*0)=f
?3in
68@fc--4--2
full=8-fc-4-c-2-f-5
search=stopped
full=(@fc,f),(fc*1,f*1,c*1)=x
same as 8-2(No.1),@cf,(x)
full=(@fc,f),(x)
2
3
in
in
78@fc--4--7--2
full=8-fc-4-c-7-f-2-f-5
search=stopped
full=(@fc,f),(fc*1, f*2, c*1)=f
same as 8-2(No.1),@cf,(x)
full=(@fc,f),(f)
3
4
in
out
88@fc--4--7--3--5@c
8-fc-4-c-7-f-3-c-5
@fc,c
(fc*1,f*1,c*2)=c
?4out

[n=9]: (?<9) :except common-path from first.
___result(3:7,9)=c(fc*4, ff=f*2, c*0), @f > @c;
___tryout : result(3:9, !(8))=c(x*1, f*5, c*0), @f > @c;
*__depth-limiter=int(sqrt(init+n=14))=3;
*____(in),depth(path) < depth-limiter : result(3:7)=c(fc*3, ff=f*2, c*0), @f > @c;
#__tryout2 : result(3:9)=c(fc*4, ff=f*3, c*0), @f > @c;
#__tryout2 : (in),depth(path) < depth-limiter : result(3:8)=c(fc*3, ff=f*3, c*0), @f > @c;
#__tryout2 : with tryout : result(3:9)=c(x*1, f*6, c*0), @f > @c;
#__tryout2 : with tryout : (in),depth(path) < depth-limiter : result(3:9),!(9))=c(x*0, f*6, c*0), @f > @c;
__fullpath : result(1:11,!(1,2,8:11))=c(x*0, f*5, c*0), @f > @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
19@c--5(@f*0,@c*1),!pair=invalid?---1in
29@fc--3@fc=stopped---1in
39@f--4--0.1--5@c
9-f-4-f-0.1-c-5
@fc
(f*2,c*1)=f
?3in
49@f--4--0.2--5@c
9-f-4-f-0.2-c-5
@fc
(f*2,c*1)=f
?3in
59@f--4--0.5--5@c
9-f-4-f-0.5-c-5
@fc
(f*2,c*1)=f
?3in
69@f--4--1--5@f
9-f-4-f-1-f-5
@ff
(f*3,c*0)=f
?3in
79@f--4--2--5@f
9-f-4-c-2-f-5
@ff
(f*2,c*1)=f
?3in
89@f--4--7--2
full=9-f-4-c-7-f-2-f-5
search=stopped
full=@ff,(f*3,c*1)=f
same as 9-4-2(No.7),@ff,(f)
full=@ff,(f)
3
4
in
out
99@f--4--7--3--5@c
9-f-4-c-7-f-3-c-5
@fc
(f*2,c*2)=x
?4out
109@f--4--7--4search=stopped,loopsame as 9-4-?(No.3-)3in
119@f--4--8@fc@fc=stopped---2in

[n=4]: ___result(1:8, !(6,8))=c((fc=cf)*4, ff=f*1, cc=c*1), @f = @c;
__tryout : result(1:7, !(6,8))=c(x*4, f*1, c*1), @f = @c;
*__depth-limiter=int(sqrt(init+n=9))=3;
*____(in),depth(path) < depth-limiter : result()=same, @f = @c;
#__tryout2 : result(1:8, !8)=c((fc=cf)*5, ff=f*1, cc=c*1), @f = @c;
#__tryout2 : with tryout : result(1:8, !8)=c(x*5, f*1, c*1), @f = @c;
__fullpath : result(1:8, !8)=c(x*4, f*2, c*1), @f > @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
14@f--0.1--5@c
4-f-0.1-c-5
@fc
(f*1,c*1)=x
?2in
24@f--0.2--5@c
4-f-0.2-c-5
@fc
(f*1,c*1)=x
?2in
34@f--0.5--5@c
4-f-0.5-c-5
@fc
(f*1,c*1)=x
?2in
44@f--1--5@f
4-f-1-f-5
@ff
(f*2,c*0)=f
?2in
54@c--2--5@f
4-c-2-f-5
@cf
(f*1,c*1)=x
?2in
64@c--7--2
full=4-c-7-f-2-f-5
search=stopped
full=@cf,(f*2,c*1)=f
same as 4-2(No.5),@cf,(x)
full=@cf,(f)
3in
74@c--7--3--5@c
4-c-7-f-3-c-5
@cc
(f*1,c*2)=c
?3in
84@fc--8@fc=stopped?1in

[n=10]: (?<10) :except common-path from first.
___result=c(2:6,8,11,12)=c((fc=cf)*6, ff=f*2, c*0), @f > @c;
___tryout : result(2:12, !(7,9,10))=c(x*1, f*6, c*1), @f > @c;
*__depth-limiter=int(sqrt(init+n=15))=3;
*____(in),depth(path) < depth-limiter : result(2:6,11,12)=c((fc=cf)*5, ff=f*2, c*0), @f > @c;
#__tryout2 : result(2:15, !(9,10))=c((fc=cf)*7, ff=f*5, c*0), @f > @c;
#__tryout2 : (in),depth(path) < depth-limiter : result(2:15, !(8,9,10))=c(fc*6, ff=f*5, c*0), @f > @c;
#__tryout2 : with tryout : result(2:15, !(9,10))=c(x*2, f*9, c*1), @f > @c;
#__tryout2 : with tryout : (in),depth(path) < depth-limiter : result(2:15, !(8,9,10))=c(x*1, f*9, c*1), @f > @c;
__fullpath : result(1:15,!(1,7:10))=c(x*0, f*7, c*3), @f > @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
110@f--5(@f*1,@c*0),!pair=invalid?---1in
210@f--4--0.1--5@c
10-f-4-f-0.1-c-5
@fc
(f*2,c*1)=f
?3in
310@f--4--0.2--5@c
10-f-4-f-0.2-c-5
@fc
(f*2,c*1)=f
?3in
410@f--4--0.5--5@c
10-f-4-f-0.5-c-5
@fc
(f*2,c*1)=f
?3in
510@f--4--1--5@f
10-f-4-f-1-f-5
@ff
(f*3,c*0)=f
?3in
610@f--4--2--5@f
10-f-4-c-2-f-5
@ff
(f*2,c*1)=f
?3in
710@f--4--7--2
full=10-f-4-c-7-f-2-f-5
search=stopped
full=@ff,(f*3,c*1)=f
same as 10-4-2(No.6),@ff,(f)
full=@ff,(f)
3
4
in
out
810@f--4--7--3--5@c
10-f-4-c-7-f-3-c-5
@fc
(f*2,c*2)=x
?4out
910@f--4--7--4search=stopped,looped same as 10-4(No.2-)3in
1010@f--4--8@fc@fc=stopped---2in
1110@f--4--9--5@c
10-f-4-f-9-c-5
@fc
(f*2,c*1)=f
?3in
1210@c--6--0.6--5@f
10-c-6-c-0.6-f-5
@cf
(f*1,c*2)=c
?3in
1310@c--6--1
full=10-c-6-c-1-f-5
search=stopped
full=@cf,(f**1,c*2)=c
same as 10-4-1(No.5),@ff,(f)
full=@cf,(c)
2
3
in
in
1410@c--6--2
full=10-c-6-f-2-f-5
search=stopped
full=@cf,(f*2,c*1)=f
same as 10-4-2(No.6),@ff,(f)
full=@cf,(f)
2
3
in
in
1510@c--6--3
full=10-c-6-c-3-c-5
search=stopped
full=@cc(f*0,c*3)=c
same as 10-4-7-3(No.8),@fc,(x)
full=@cc,(c)
2
3
in
in

[n=11]: (?<11) :except common-path from first.
___result(1:5,7,10,11,13)=c((@f*1,@c*0)=invalid?, cf*3, ff=f*1, cc=c*5), @f < @c;
___tryout : result(1:13, !(6,8,9))=c(x*0, f*3, c*6), @f < @c;
*__depth-limiter=int(sqrt(init+n=16))=4;
*____(in),depth(path) < depth-limiter : result=same, @f < @c;
#__tryout2 : result(1:19, !(8,9,12))=c(cf*8, ff=f*1, cc=c*7), result(20)=c(cf*4, f*0, cc=c*5), sum=c(cf*12, ff=f*1, cc=c*12), @f < @c;
#__tryout2 : with tryout : result(1:19, !(8,9,12))=c(x*0, f*5, c*11), result(20)=c(x*0, f*2, c*7), sum=c(x*0, f*7, c*18), @f < @c:
__fullpath : result(1:20, !(8,9,12))=c(x*2, f*8, c*13), @f < @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
111@c--4--0.1--5@c
11-c-4-f-0.1-c-5
@cc
(f*1,c*2)=c
?3in
211@c--4--0.2--5@c
11-c-4-f-0.2-c-5
@cc
(f*1,c*2)=c
?3in
311@c--4--0.5--5@c
11-c-4-f-0.5-c-5
@cc
(f*1,c*2)=c
?3in
411@c--4--1--5@f
11-c-4-f-1-f-5
@cf
(f*2,c*1)=f
?3in
511@c--4--2--5@f
11-c-4-c-2-f-5
@cf
(f*1,c*2)=c
?3in
611@c--4--7--2
full=11-c-4-c-7-f-2-f-5
search=stopped
full=@cf,(f*2,c*2)=x
same as 11-4-2(No.5),@cf,(c)
full=@cf,(x)
3
4
in
in
711@c--4--7--3--5@c
11-c-4-c-7-f-3-c-5
@cc
(f*1,c*3)=c
?4in
811@c--4--7--4 search=stopped,loopedsame as 11-4-(No.1)3in
911@c--4--8@fc@fc=stopped---2in
1011@c--4--9--5@c
11-c-4-f-9-c-5
@cc
(f*1,c*2)=c
?3in
1111@c--4--10--5@f
11-c-4-f-10-f-5
@cf
(f*2,c*1)=f
?3in
1211@f--5(@f*1,@c*0),!pair=invalid?---1in
1311@f--6--0.6--5@f
11-f-6-c-0.6-f-5
@ff
(f*2,c*1)=f
?3in
1411@f--6--1
full=11-f-6-c-1-f-5
search=stopped
full=@ff,(f*2,c*1)=f
same as 11-4-1(No.4),@cf,(f)
full=@ff,(f)
2
3
in
in
1511@f--6--2
full=11-f-6-f-2-f-5
search=stopped
full=@ff,(f*3,c*0)=f
same as 11-4-2(No.5),@cf,(c)
full=@ff,(f)
2
3
in
3
1611@f--6--3
full=11-f-6-c-3-c-5
search=stopped
full=@fc,(f*1,c*2)=c
same as 11-4-7-3(No.7),@cc,(c)
full=@fc,(c)
2
3
in
in
1711@f--6--10
full=11-f-6-c-10-f-5
search=stopped
full=@ff,(f*2,c*1)=f
same as 11-4-10(No.11),@cf,(f)
full=@ff,(f)
2in
1811@c--7--2
full=11-c-7-f-2-f-5
search=stopped
full=@cf,(f*2,c*1)=f
same as 11-4-2(No.5),@cf,(c)
full=cf,(f)
2in
1911@c--7--3
full=11-c-7-f-3-c-5
search=stopped
full=@cc,(f*1,c*2)=c
same as 11-4-7-3(No.7),@cc,(c)
full=@cc,(c)
2in
2011@c--7--4
[1]full=11-c-7-c-4-f-0.1-c-5
[2]full=11-c-7-c-4-f-0.2-c-5
[3]full=11-c-7-c-4-f-0.5-c-5
[4]full=11-c-7-c-4-f-1-f-5
[5]full=11-c-7-c-4-c-2-f-5
[6]full=11-c-7-c-4--7,loop
[7]full=11-c-7-c-4-fc-8
[8]full=11-c-7-c-4-f-9-c-5
[9]full=11-c-7-c-4-f-10-f-5
search=stopped
[1]full=@cc,(f*1,c*3)=c
[2]full=@cc,(f*1,c*3)=c
[3]full=@cc,(f*1,c*3)=c
[4]full=@cf,(f*2,c*1)=f
[5]full=@cc,(f*1,c*3)=c
[6]full=
[7]@fc=stopped
[8]full=@cc,(f*1,c*3)=c
[9]full=@cf,(f*2,c*2)=x
same as 11-4-(No.1:11),@cc,(c)
[1]full=@cc,(c)
[2]full=@cc,(c)
[3]full=@cc,(c)
[4]full=@cf,(f)
[5]full=@cc,(c)
[6]full=
[7]full=
[8]full=@cc,(c)
[9]full=@cf,(x)
2
[1]4
[2]4
[3]4
[4]4
[5]4
[6]
[7]
[8]4
[9]4
in
[1]in
[2]in
[3]in
[4]in
[5]in
[6]
[7]
[8]in
[9]in

[n=13]: (?<13) :except common-path from first.
___result(1:6,9:11,15)=c(fc*5, ff=f*5, c*0), @f > @c;
___tryout : result(1:15, !(7,8,12:14))=c(x*4, f*5, c*1), @f > @c;
*__depth-limiter=int(sqrt(init+n=18))=4;
*____(in),depth(path) < depth-limiter : result=same, @f > @c;
#__tryout2 : result(1:20, !(14,20))=c(fc*6, ff=f*12, c*0), @f > @c;
#__tryout2 : with tryout : result(1:20, !(14,20))=c(x*5, f*12, c*1), @f > @c;
__fullpath : result(1:20, !(14,20))=c(x*6, f*10,c*2), @f > @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
113@f--6--0.6--5@f
13-f-6-c-0.6-f-5
@ff
(f*2,c*1)=f
?3in
213@f--6--1--5@f
13-f-6-c-1-f-5
@ff
(f*2,c*1)=f
?3in
313@f--6--2--5@f
13-f-6-f-2-f-5
@ff
(f*3,c*0)=f
?3in
413@f--6--3--5@c
13-f-6-c-3-c-5
@fc
(f*1,c*2)=c
?3in
513@f--6--10--5@f
13-f-6-c-10-f-5
@ff
(f*2,c*1)=f
?3in
613@f--6--11--5@f
13-f-6-f-11-f-5
@ff
(f*3,c*0)=f
?3in
713@f--7--2
full=13-f-7-f-2-f-5
search=stopped
full=@ff,(f*3,c*0)=f
same as 13-6-2(No.3),@ff,(f)
full=@ff,(f)
2
3
in
in
813@f--7--3
full=13-f-7-f-3-c-5
search=stopped
full=@fc,(f*2,c*1)=f
same as 13-6-3(No.4),@fc,(c)
full=@fc,(f)
2
3
in
in
913@f--7--4--0.1--5@c
13-f-7-c-4-f-0.1-c-5
@fc
(f*2,c*2)=x
?4in
1013@f--7--4--0.2--5@c
13-f-7-c-4-f-0.2-c-5
@fc
(f*2,c*2)=x
?4in
1113@f--7--4--0.5--5@c
13-f-7-c-4-f-0.5-c-5
@fc
(f*2,c*2)=x
?4in
1213@f--7--4--1
full=13-f-7-c-4-f-1-f-5
search=stopped
full=@ff,(f*3,c*1)=f
same as 13-6-1(No.2),@ff,(f)
full=@ff,(f)
3
4
in
in
1313@f--7--4--2
full=13-f-7-c-4-c-2-f-5
search=stopped
full=@ff,(f*2,c*2)=x
same as 13-6-2(No.3),@ff,(f)
full=@ff,(x)
3
4
in
in
1413@f--7--4--8@fc@fc=stopped---3in
1513@f--7--4--9--5@c
13-f-7-c-4-f-9-c-5
@fc
(f*2,c*2)=x
?4in
1613@f--7--4--10
full=13-f-7-c-4-f-10-f-5
search=stopped
full=@ff,(f*3,c*1)=f
same as 13-6-10(No.5),@ff,(f)
full=@ff,(f)
3
4
in
in
1713@f--7--4--11
full=13-f-7-c-4-c-11-f-5
search=stopped
full=@ff,(f*2,c*2)=x
same as 13-6-11(No.6),@ff,(f)
full=@ff,(x)
3
4
in
in
1813@f--7--11
full=13-f-7-c-11-f-5
search=stopped
full=@ff,(f*2,c*1)=f
same as 13-6-11(No.6),@ff,(f)
full=@ff,(f)
2
3
in
in
1913@c--8--2
full=13-c-8-c-2-f-5
search=stopped
full=@cf,(f*1,c*2)=c
same as 13-6-2(No.3),@ff,(f)
full=@cf,(c)
2
3
in
in
2013@c--8--4@fc@fc=stopped---2in

[n=17]: (?<17) :result(1:3)=c((fc=cf)*2, ff=f*1, c*0), @f > @c;
___common:none;
*__depth-limiter=int(sqrt(init+n=22))=4;
*____(in),depth(path) < depth-limiter : result(1:3)=same, @f > @c;
___fullpath() : result(1:3)=same, @f > @c;
No.path(n to init)fc
status
common
path
depth
(path)
depth(path)
.vs.limiter
117@f--9--5@c@fcx2in
217@f--10--5@f@ffx2in
317@c--11--5@f@cfx2in

[n=19]: (?<19) :except common-path from first.
___result(1:6,7,8,11:13,17)=c(cf*4, ff=f*1, cc=c*5), @f < @c; expected=!(@f < @c);
___tryout : collect all (f,c) of branches : パス内での大小関係で判定する。
____________result(1:6,7,8,11:13,17)=c(cf=x*3, f*2, c*5), @f < @c; expected=!(@f < @c);
*__depth-limiter=int(sqrt(init+n=24))=4;
*____(in),depth(path) < depth-limiter : result(1:6)=c(cf*4, ff=f*1, cc=c*1), @f = @c; expected.
*____(in),depth(path) < depth-limiter : result(tryout;1:6)=c(cf=x*3, ff=f*2, cc=c*1), @f > @c; expected.
#__tryout2 : result(1:22, !(16,22))=c(cf*10, ff=f*4, cc=c*6), @f < @c;
#__tryout2 : (in),depth(path) < depth-limiter : result(1:22, !(11:13,16,17,22))=c(cf*10, ff=f*4, cc=c*2), @f > @c;
#__tryout2 : with tryout : result(1:22, !(16,22))=c(x*10, f*4, c*6), @f < @c;
#__tryout2 : with tryout : (in),depth(path) < depth-limiter : result(1:22, !(11:13,16,17,22))=c(cf*10, ff=f*4, cc=c*2), @f > @c;
__fullpath : result(1:22, !(16,22, out=c(11:15,17:19)))=c(x*6, f*4, c*2), @f > @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
119@c--10--5@f@cf=x?2in
219@f--11--5@f@ff=f?2in
319@c--13--6--0.6--5@f
19-c-13-f-6-c-0.6-f-5
@cf=x
(f*2,c*2)=x
?
tryout
4in
419@c--13--6--1--5@f
19-c-13-f-6-c-1-f-5
@cf=x
(f*2,c*2)=x
?
tryout
4in
519@c--13--6--2--5@f
19-c-13-f-6-f-2-f-5
@cf=x
(f*3,c*1)=f
?
tryout
4in
619@c--13--6--3--5@c
19-c-13-f-6-c-3-c-5
@cc=c
(f*1,c*3)=c
?
tryout
4in
719@c--13--6--10
full=19-c-13-f-6-c-10-f-5
search=stopped
full=@cf,(f*2,c*2)=x
same as 19-10(No.1),@cf,(x)
full=@cf,(x)
3in
819@c--13--6--11
full=19-c-13-f-6-f-11-f-5
search=stopped
full=@cf,(f*3,c*1)=f
same as 19-11(No.2),@ff,(f)
full=@cf,(f)
3in
919@c--13--7--2
full=19-c-13-f-7-f-2-f-5
search=stopped
full=@cf,(f*3,c*1)=f
same as 19-13-6-2(No.5),@cf,(x)
full=@cf,(f)
3
4
in
in
1019@c--13--7--3
full=19-c-13-f-7-f-3-c-5
search=stopped
full=@cc,(f*2,c*2)=x
same as 19-13-6-3(No.6),@cc,(c)
full=@cc,(x)
3
4
in
in
1119@c--13--7--4--0.1--5@c
19-c-13-f-7-c-4-f-0.1-c-5
@cc=c
(f*2,c*3)=c
?
tryout
5out
1219@c--13--7--4--0.2--5@c
19-c-13-f-7-c-4-f-0.2-c-5
@cc=c
(f*2,c*3)=c
?
tryout
5out
1319@c--13--7--4--0.5--5@c
19-c-13-f-7-c-4-f-0.5-c-5
@cc=c
(f*2,c*3)=c
?
tryout
5out
1419@c--13--7--4--1
full=19-c-13-f-7-c-4-f-1-f-5
search=stopped
full=@cf,(f*3,c*2)=f
same as 19-13-6-1(No.4),@cf,(x)
full=@cf,(f)
4
5
in
out
1519@c--13--7--4--2
full=19-c-13-f-7-c-4-c-2-f-5
search=stopped
full=@cf,(f*2,c*3)=c
same as 19-13-6-2(No.5),@cf,(x)
full=@cf,(c)
4
5
in
out
1619@c--13--7--4--8@fc@fc=stopped---4in
1719@c--13--7--4--9--5@c
19-c-13-f-7-c-4-f-9-c-5
@cc=c
(f*2,c*3)=c
?
tryout
5out
1819@c--13--7--4--10
full=19-c-13-f-7-c-4-f-10-f-5
search=stopped
full=@cf,(f*3,c*2)=f
same as 19-10(No.1),@cf,(x)
full=@cf,(f)
4
5
in
out
1919@c--13--7--4--11
full=19-c-13-f-7-c-4-c-11-f-5
search=stopped
full=@cf,(f*2,c*3)=c
same as 19-11(No.2),@ff,(f)
full=@cf,(c)
4
5
in
out
2019@c--13--7--11
full=19-c-13-f-7-c-11-f-5
search=stopped
full=@cf,(f*2,c*2)=x
same as 19-11(No.2),@ff,(f)
full=@cf,(x)
3
4
in
in
2119@c--13--8--2
full=19-c-13-c-8-c-2-f-5
search=stopped
full=@cf,(f*1,c*3)=c
same as 19-13-6-2(No.5),@cf,(x)
full=@cf,(c)
3
4
in
in
2219@c--13--8--4@fc@fc=stopped---3in

[n=23]: (?<23) :except common-path from first.
___result(1:6,9:11,15)=c(cf*5, f*0, cc=c*5), @f < @c; expected=!(@f < @c);)
___tryout : result(1:6,9:11,15)=c(fc*3, f*2, c*5), @f < @c; expected=!(@f < @c);
*__depth-limiter=int(sqrt(init+n=28))=5;
*____(in),depth(path) < depth-limiter : result()=same, @f < @c; expected=!(@f < @c);
#__tryout2 : result(1:22, !(14,20))=c(cf*14, f*0, cc=c*6), @f < @c; expected=!(@f < @c);
#__tryout2 : with tryout : result(1:22, !(14,20))=c(fc=x*6, f*8, c*6), @f > @c; happy?
__fullpath : result(1:22, !(14,20))=c(x*6, f*5, c*9), @f < @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
123@c--13--6--0.6--5@f
23-c-13-f-6-c-0.6-f-5
@cf
(f*2,c*2)=x
?4in
223@c--13--6--1--5@f
23-c-13-f-6-c-1-f-5
@cf
(f*2,c*2)=x
?4in
323@c--13--6--2--5@f
23-c-13-f-6-f-2-f-5
@cf
(f*3,c*1)=f
?4in
423@c--13--6--3--5@c
23-c-13-f-6-c-3-c-5
@cc
(f*1,c*3)=c
?4in
523@c--13--6--10--5@f
23-c-13-f-6-c-10-f-5
@cf
(f*2,c*2)=x
?4in
623@c--13--6--11--5@f
23-c-13-f-6-f-11-f-5
@cf
(f*3,c*1)=f
?4in
723@c--13--7--2
full=23-c-13-f-7-f-2-f-5
search=stopped
full=@cf,(f*3,c*1)=f
same as 23-13-6-2(No.3),@cf,(f)
full=@cf,(f)
3
4
in
in
823@c--13--7--3
full=23-c-13-f-7-f-3-c-5
search=stopped
full=@cc(f*2,c*2)=x
same as 23-13-6-3(No.4),@cc,(c)
full=@cc,(x)
3
4
in
in
923@c--13--7--4--0.1--5@c
23-c-13-f-7-c-4-f-0.1-c-5
@cc
(f*2,c*3)=c
?5in
1023@c--13--7--4--0.2--5@c
23-c-13-f-7-c-4-f-0.2-c-5
@cc
(f*2,c*3)=c
?5in
1123@c--13--7--4--0.5--5@c
23-c-13-f-7-c-4-f-0.5-c-5
@cc
(f*2,c*3)=c
?5in
1223@c--13--7--4--1
full=23-c-13-f-7-c-4-f-1-f-5
search=stopped
full=@cf,(f*3,c*2)=f
same as 23-13-6-1(No.2),@cf,(x)
full=@cf,(f)
4
5
in
in
1323@c--13--7--4--2
full=23-c-13-f-7-c-4-c-2-f-5
search=stopped
full=@cf,(f*2,c*3)=c
same as 23-13-6-2(No.3),@cf,(f)
full=@cf,(c)
4
5
in
in
1423@c--13--7--4--8@fc@fc=stopped?4in
1523@c--13--7--4--9--5@c
23-c-13-f-7-c-4-f-9-c-5
@cc
(f*2,c*3)=c
?5in
1623@c--13--7--4--10
full=23-c-13-f-7-c-4-f-10-f-5
search=stopped
full=@cf,(f*3,c*1)=f
same as 23-13-6-10(No.5),@cf,(x)
full=@cf,(f)
4
5
in
in
1723@c--13--7--4--11
full=23-c-13-f-7-c-4-c-11-f-5
search=stopped
full=@cf,(f*2,c*3)=c
same as 23-13-6-11(No.6),@cf,(f)
full=@cf,(c)
4
5
in
in
1823@c--13--7--11
full=23-c-13-f-7-c-11-f-5
search=stopped
full=@cf,(f*2,c*2)=x
same as 23-13-6-11(No.6),@cf,(f)
full=@cf,(x)
3
4
in
in
1923@c--13--8--2
full=23-c-13-c-8-c-2-f-5
search=stopped
full=@cf,(f*1,c*3)=c
same as 23-13-6-2(No.3),@cf,(f)
full=@cf,(c)
3
4
in
in
2023@c--13--8--4@fc@fc=stopped---3in
2123@c--13--19--10
full=23-c-13-c-19-c-10-f-5
search=stopped
full=@cf,(f*1,c*3)=c
same as 23-13-6-10(No.5),@cf,(x)
full=@cf,(c)
3
4
in
in
2223@c--13--19--11
full=23-c-13-c-19-f-11-f-5
search=stopped
full=@cf,(f*2,c*2)=x
same as 23-13-6-11(No.6),@cf,(f)
full=@cf,(x)
3
4
in
in

[n=29]: (?<29) :result(1:6,11:13,17,18)=c(fc*5, ff=f*6, c*0), @f > @c;
*__depth-limiter=int(sqrt(init+n=34))=5;
*____(in),depth(path) < depth-limiter : result(1:6)=c(fc*1, ff=f*6, c*0), @f > @c;
#__tryout2 : result(1:20, !(16,20))=c(fc*6, ff=f*12, c*0), @f > @c;
#__tryout2 : (in),depth(path) < depth-limiter : result(1:20, !(11:13,16,17,20))=c(fc*2, ff=f*12, c*0), @f > @c;
#__tryout2 : with tryout : result(1:20, !(16,20))=c(x*4, f*12, c*2), @f > @c;
#__tryout2 : with tryout : (in),depth(path) < depth-limiter : result(1:20, !(11:13,16,17,20))=c(x*0, f*12, c*2), @f > @c;
___fullpath : result(1:20, !(16,20, out=c(11:15,17)))=c(x*1, f*10, c*2), @f > @c;
No.path(n to init)fc
status
common-path,
fc-copied,(tryout)
depth
(path)
depth(path)
.vs.limiter
129@f--19--10--5@f
29-f-19-c-10-f-5
@ff
(f*2,c*1)=f
?3in
229@f--19--11--5@f
29-f-19-f-11-f-5
@ff
(f*3,c*0)=f
?3in
329@f--19--13--6--0.6--5@f
29-f-19-c-13-f-6-c-0.6-f-5
@ff
(f*3,c*2)=f
?5in
429@f--19--13--6--1--5@f
29-f-19-c-13-f-6-c-1-f-5
@ff
(f*3,c*2)=f
?5in
529@f--19--13--6--2--5@f
29-f-19-c-13-f-6-f-2-f-5
@ff
(f*4,c*1)=f
?5in
629@f--19--13--6--3--5@c
29-f-19-c-13-f-6-c-3-c-5
@fc
(f*2,c*3)=c
?5in
729@f--19--13--6--10
full=29-f-19-c-13-f-6-c-10-f-5
search=stopped
@ff,(f*3,c*2)=f
same as 29-19-10(No.1),@ff,(f)
full=@ff,(f)
4
5
in
in
829@f--19--13--6--11
full=29-f-19-c-13-f-6-f-11-f-5
search=stopped
full=@ff,(f*4,c*1)=f
same as 29-19-11(No.2),@ff,(f)
full=@ff,(f)
4
5
in
in
929@f--19--13--7--2
full=29-f-19-c-13-f-7-f-2-f-5
search=stopped
full=@ff,(f*4,c*1)=f
same as 29-19-13-6-2(No.5),@ff,(f)
full=@ff,(f)
4
5
in
in
1029@f--19--13--7--3
full=29-f-19-c-13-f-7-f-3-c-5
search=stopped
full=@fc,(f*3,c*2)=f
same as 29-19-13-6-3(No.6),@fc,(c)
full=@fc,(f)
4
5
in
in
1129@f--19--13--7--4--0.1--5@c
29-f-19-c-13-f-7-c-4-f-0.1-c-5
@fc
(f*3,c*3)=x
?6out
1229@f--19--13--7--4--0.2--5@c
29-f-19-c-13-f-7-c-4-f-0.2-c-5
@fc
(f*3,c*3)=x
?6out
1329@f--19--13--7--4--0.5--5@c
29-f-19-c-13-f-7-c-4-f-0.5-c-5
@fc
(f*3,c*3)=x
?6out
1429@f--19--13--7--4--1
full=29-f-19-c-13-f-7-c-4-f-1-f-5
search=stopped
full=@ff,(f*4,c*2)=f
same as 29-19-13-6-1(No.4),@ff,(f)
full=@ff,(f)
5
6
in
out
1529@f--19--13--7--4--2
full=29-f-19-c-13-f-7-c-4-c-2-f-5
search=stopped
full=@ff,(f*3,c*3)=x
same as 29-19-13-6-2(No.5),@ff,(f)
full=@ff,(x)
5
6
in
out
1629@f--19--13--7--4--8@fc@fc=stopped---5in
1729@f--19--13--7--4--9--5@c
29-f-19-c-13-f-7-c-4-f-9-c-5
@fc
(f*3,c*3)=x
?6out
1829@f--19--13--7--11--5@f
29-f-19-c-13-f-7-c-11-f-5
@ff
(f*3,c*2)=f
?5in
1929@f--19--13--8--2
full=29-f-19-c-13-c-8-c-2-f-5
search=stopped
full=@ff,(f*2,c*3)=c
same as 29-19-13-6-2(No.5),@ff,(f)
full=@ff,(c)
4
5
in
in
2029@f--19--13--8--4@fc@fc=stopped---4in

[n=all]: resut is; as init=5;
org=!depth-limiter*depth-limiter*tryout2
use common-path, fullpath()=used !common-path.
nfc
status
(all)
fc
status
(common)
init=5
group
comment *fc
status
(all)
init=5
group
*rate
com*
path,%
(!out)
fc
status
(all),
(out,tryout)
init=5
group
comment
5f:3<@c:4---oinit *same as orgo *0%,0/12
(same)
same as org
tryout=(@f:3 <@c:4)
fullpath(tryout,out)=(@f:3 <@c:4)
o
o
o
path.top=
(f=3/7,c=4/7)
6f:1=@c:1---x *samex *0%,0/4
(same)
same
tryout=(same)
fullpath()=same
x
x
x
path.top=
(f=1/2,c=1/2)
7f:1<@c:3f:1<@c:3o
o

tryout
*sameo *14%,1/7
(same)
@f:2 <@c:3
tryout=(@f:3=@c:3)
fullpath()=(@f:2 <@c:4)
o
x
o
path.top=
(f=2/7,c=5/7)
8f:2<@c:3
f:1>@c:0
f:1=c:1
f:1<@c:3
.
o
x
x
.
tryout
tryout
*f:1<@c:3o *16%,1/6
(same)
@f:1 < @c:4
@f:1 < @c:3
tryout=(@f:1=@c:1)
tryout.out=(@f:1 > @c:0)
fullpath()=(@f:1 > @c:0)
=>applied [h]{3-2}. @f:1<@c:4
o
o
x
x
x
o
path.top=
(fc=5/6,f=0/6,c=1/6)
---
todo:handling @fc?
=>See [h].
9f:2>@c:0
f:5>@c:0
---x
x
.
tryout
*f:2>@c:0x *10%,1/10
(11%,1/9)
@f:3>@c:0
out=(@f:3>@@c:0)
tryout=(@f:6>@c:0)
tryout,out=(@f:6>@c:0)
fullpath()=(@f:5>@c:0)
applied [d-3],n=4:c(f=c,f>@c).
x
x
x
x
x
path.top=
(fc=1/10,f=8/10,c=1/10)
@fc(1)=stopped,
@c(1)=invalid.(top=f:n>c:0)?

check 9-4-*.
10f:2>@c:0
f:6>@c:1
---x
x
.
tryout
*f:2>@c:0x *28%,4/14
(23%,3/13)
@f:5>@c:0
out=(@f:5>@c:0)
tryout=(@f:9>@c:1)
tryout,out=(@f:9>@c:1)
fullpath()=(@f:7>@c:3)
x
x
x
x
x
path.top=
(f=10/14,c=4/14:28%)
11f:1<@c:5
f:3<@c:6
---o
o

tryout
*f:3<@c:6o *42%,8/19
(same)
@f:1<@c:12
tryout=(@f:7<@c:18)
fullpath()=(@f:8<@c:13)
o
o
o
path.top=
(f=6/26,c=20/26)
13f:5>@c:0
f:5>@c:1
---x
x
.
tryout
*samex *40%,8/20
(same)
@f:12 >@c:0
tryout=(@f:12 >@c:1)
fullpath()=(@f:10 >@c:2)
x
x
x
path.top=
(f*18/20,c=2/20:10%)
17f:1>@c:0---x *samex *0%,0/3
(same)
same
tryout=(same)
fullpath()=same
x
x
x
path.top=
(f=2/3,c=1/3)
19f:1<@c:5
f:2<@c:5
---o?
o?
?
tryout
*f:1=@c:1
f:2>@c:1:tryout
x
x
*45%,10/22
(55%,10/18)
@f:4 < @c:6
out=(@f:4 > @c:2)
tryout=(@f:4 < @c:6)
tryout,out=(@f:4 > @c:2)
fullpath()=(@f:4 > @c:2)
applied [d-2],n=c(10,11,13): @f > @c;
o?
x
o?
x
x
path.top=19-10-*:f>@c
path.top=19-11-*:f<@c
path.top=19-13-*:f>@c
(f=1/22:4.5%,c=21/22)
23f:0<@c:5---o? *f:2<@c:5o? *45%,10/22
(same)
@f:0 < @c:6
tryout=(@f:8 > @c:6)
fullpath()=(@f:5 < @c:9)
applied [d-1],n=13:@f>@c
o?
x
o?
x
path.top=23-13-*
=(f=0/22,c=22/22)
=>applied [d-1],n=13.
29f:6>@c:0---x *f:6>@c:0x *35%,7/20
(43%,7/16)
f:12>@c:0
out=(f:12>@c:0)
tryout=(@f:12 > @c:2)
tryout,out=(@f:12 > @c:2)
fullpath(tryout,out)=(f:10>@c:2)
applied [d-1],n=19:@f > @c
x
x
x
x
x
x
path.top=29-19-*
=(f=20/20,c=0/20)
=>applied [d-1],n=19.
So, init=5 : @expected=c(5,7,8,11);
__[org] border=c(5,7,8,11,19?,23?); @!happy.
__[depth-limiter] border=c(5,7,8,11,23?); @!happy.
__[tryout2 :use common-path (same as...)] border=c(5,7,8,11,19?,23?, ...); @!happy.
__[tryout2 :with tryout, out=depth-limiter] border=c(5,7?,8?,11); happy? @自然は細部にこだわる...Nature pays attention to details...
__[fullpath(tryout2; tryout,out),偏りを嫌う] border=c(5,7,8,11); @by c(d-1, d-2, d-3, h)

end...
---
2022/12/03 : started to edit.
2022/12/05 : added common-path. fixed n=c(6,7,8,9,17). added n=c(all).
2022/12/06 : added c([4][f], n=c(5)).
2022/12/07 : fixed n=c(10,11,13), tryout n=c(19).
2022/12/08-09-10 : added c([4][g]). applied depth-limiter for n=all.
2022/12/10 : Finally, n=23 left. A problem occurred while working on it.
2022/12/11-14 : modified c([4][c], [4][e], [4][g]). redid n=all for tryout2. n=c(7,8) is not expected.
2022/12/14,15 : added c([4][c-3],[d-1]). (TODO) redo n=all for fullpath().
2022/12/18 : added c([4][d-2][d-3]).
2022/12/26-27 : added c([4][h],[i]).長かったけれど、楽しめました。ありがとう。
---
(TODO)3つの世界は存在するか? 素数の世界も島があり、分断されている?
(TODO) three worlds exist? The world of prime numbers also has islands and is divided?
@子(border)は親(init)に似るということか? {@偏り嫌い(偏ったら、更に内側を見る), @全パスの多数決で判断...}
__init(@f = @c) : border()=all(@f = @c); init=c(?);
__init(@f > @c) : border()=all(@f > @c); init=c(?);
__init(@f < @c) : border()=all(@f < @c); init=c(5,...);
---