高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (979ﾚｽ)
上下前次1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
抽出解除必死ﾁｪｯｶｰ(本家) (べ) 自ID ﾚｽ栞あぼーん

102: １３２人目の素数さん [sage] 2024/08/20(火) 05:30:38.98 ID:O+DDQLmu

"
n=11;
pn={jan[n,1]};
Total@Flatten@Table[jan[n,x1]jan[x1,1],{x1,2,n}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,1],{x1,2,n},{x2,2,x1}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,1],{x1,2,n},{x2,2,x1},{x3,2,x2}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3}]//AppendTo[pn,#]&;
"
str=NULL
str[1]="pn={jan[n,1]};"
str[2]="Total@Flatten@Table[jan[n,x1]jan[x1,1],{x1,2,n}]//AppendTo[pn,#]&;"
str[3]="Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,1],{x1,2,n},{x2,2,x1}]//AppendTo[pn,#]&;"
str[4]="Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,1],{x1,2,n},{x2,2,x1},{x3,2,x2}]//AppendTo[pn,#]&;"
str[5]="Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3}]//AppendTo[pn,#]&;"
for(i in 2:30){
y=paste0(",x",i,"]jan[x",i,",1],")
tmp=sub(",1],",y,str[i])
z=paste0("},{x",i,",2,x",i-1,"}]")
str[i+1]=sub("}]",z,tmp)
}

http://rio2016.5ch.net/test/read.cgi/math/1723152147/102

103: １３２人目の素数さん [sage] 2024/08/20(火) 08:08:58.34 ID:O+DDQLmu

jan[n_,m_] := (
If[m==0 || m>n, Return[0]];
If[m==n,1 - 3*(2^n-2)/3^n,3*Binomial[n,m]/3^n]
)
n=11;
pn={jan[n,1]};
Total@Flatten@Table[jan[n,x1]jan[x1,1],{x1,2,n}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,1],{x1,2,n},{x2,2,x1}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,1],{x1,2,n},{x2,2,x1},{x3,2,x2}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,x5]jan[x5,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3},{x5,2,x4}]//AppendTo[pn,#]&;
...
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,x5]jan[x5,x6]jan[x6,x7]jan[x7,x8]jan[x8,x9]jan[x9,x10]jan[x10,x11]jan[x11,x12]jan[x12,x13]jan[x13,x14]jan[x14,x15]jan[x15,x16]jan[x16,x17]jan[x17,x18]jan[x18,x19]jan[x19,x20]jan[x20,x21]jan[x21,x22]jan[x22,x23]jan[x23,x24]jan[x24,x25]jan[x25,x26]jan[x26,x27]jan[x27,x28]jan[x28,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3},{x5,2,x4},{x6,2,x5},{x7,2,x6},{x8,2,x7},{x9,2,x8},{x10,2,x9},{x11,2,x10},{x12,2,x11},{x13,2,x12},{x14,2,x13},{x15,2,x14},{x16,2,x15},{x17,2,x16},{x18,2,x17},{x19,2,x18},{x20,2,x19},{x21,2,x20},{x22,2,x21},{x23,2,x22},{x24,2,x23},{x25,2,x24},{x26,2,x25},{x27,2,x26},{x28,2,x27}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,x5]jan[x5,x6]jan[x6,x7]jan[x7,x8]jan[x8,x9]jan[x9,x10]jan[x10,x11]jan[x11,x12]jan[x12,x13]jan[x13,x14]jan[x14,x15]jan[x15,x16]jan[x16,x17]jan[x17,x18]jan[x18,x19]jan[x19,x20]jan[x20,x21]jan[x21,x22]jan[x22,x23]jan[x23,x24]jan[x24,x25]jan[x25,x26]jan[x26,x27]jan[x27,x28]jan[x28,x29]jan[x29,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3},{x5,2,x4},{x6,2,x5},{x7,2,x6},{x8,2,x7},{x9,2,x8},{x10,2,x9},{x11,2,x10},{x12,2,x11},{x13,2,x12},{x14,2,x13},{x15,2,x14},{x16,2,x15},{x17,2,x16},{x18,2,x17},{x19,2,x18},{x20,2,x19},{x21,2,x20},{x22,2,x21},{x23,2,x22},{x24,2,x23},{x25,2,x24},{x26,2,x25},{x27,2,x26},{x28,2,x27},{x29,2,x28}]//AppendTo[pn,#]&;
Total@Flatten@Table[jan[n,x1]jan[x1,x2]jan[x2,x3]jan[x3,x4]jan[x4,x5]jan[x5,x6]jan[x6,x7]jan[x7,x8]jan[x8,x9]jan[x9,x10]jan[x10,x11]jan[x11,x12]jan[x12,x13]jan[x13,x14]jan[x14,x15]jan[x15,x16]jan[x16,x17]jan[x17,x18]jan[x18,x19]jan[x19,x20]jan[x20,x21]jan[x21,x22]jan[x22,x23]jan[x23,x24]jan[x24,x25]jan[x25,x26]jan[x26,x27]jan[x27,x28]jan[x28,x29]jan[x29,x30]jan[x30,1],{x1,2,n},{x2,2,x1},{x3,2,x2},{x4,2,x3},{x5,2,x4},{x6,2,x5},{x7,2,x6},{x8,2,x7},{x9,2,x8},{x10,2,x9},{x11,2,x10},{x12,2,x11},{x13,2,x12},{x14,2,x13},{x15,2,x14},{x16,2,x15},{x17,2,x16},{x18,2,x17},{x19,2,x18},{x20,2,x19},{x21,2,x20},{x22,2,x21},{x23,2,x22},{x24,2,x23},{x25,2,x24},{x26,2,x25},{x27,2,x26},{x28,2,x27},{x29,2,x28},{x30,2,x29}]//AppendTo[pn,#]&;
pn
Accumulate[pn]
% // N

http://rio2016.5ch.net/test/read.cgi/math/1723152147/103

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