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
抽出解除ﾚｽ栞

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

768: １３２人目の素数さん [sage] 2025/03/25(火) 20:20:38.34 ID:JvJVqzfB

mat1=t(apply(ans1,1, \(x) c(x,fn_rest(v,x))))
M1=matrix(c("赤","黒","白","青")[mat1],ncol=10) |> noquote()
L1=cbind(M1[,1],'|',M1[,2],'|',M1[,3:10]) |> noquote() ; L1

mat2=t(apply(ans2,1, \(x) c(x,fn_rest(v,x))))
M2=matrix(c("赤","黒","白","青")[mat2],ncol=10) |> noquote()
L2=cbind(M2[,1],'|',M2[,2:3],'|',M2[,4:10]) |> noquote() ; L2

mat3=t(apply(ans3,1, \(x) c(x,fn_rest(v,x))))
M3=matrix(c("赤","黒","白","青")[mat3],ncol=10) |> noquote()
L3=cbind(M3[,1],'|',M3[,2:4],'|',M3[,5:10]) |> noquote() ; L3

mat4=t(apply(ans4,1, \(x) c(x,fn_rest(v,x))))
M4=matrix(c("赤","黒","白","青")[mat4],ncol=10) |> noquote()
L4=cbind(M4[,1],'|',M4[,2:5],'|',M4[,6:10]) |> noquote() ; L4

mat5=t(apply(ans5,1, \(x) c(x,fn_rest(v,x))))
M5=matrix(c("赤","黒","白","青")[mat5],ncol=10) |> noquote()
L5=cbind(M5[,1:2],'|',M5[,3:4],'|',M5[,5:10]) |> noquote() ; L5

mat6=t(apply(ans6,1, \(x) c(x,fn_rest(v,x))))
M6=matrix(c("赤","黒","白","青")[mat6],ncol=10) |> noquote()
L6=cbind(M6[,1:2],'|',M6[,3:5],'|',M6[,6:10]) |> noquote() ; L6

mat7=t(apply(ans7,1, \(x) c(x,fn_rest(v,x))))
M7=matrix(c("赤","黒","白","青")[mat7],ncol=10) |> noquote()
L7=cbind(M7[,1:2],'|',M7[,3:5],'|',M7[,6:10]) |> noquote() ; L7

mat8=t(apply(ans8,1, \(x) c(x,fn_rest(v,x))))
M8=matrix(c("赤","黒","白","青")[mat8],ncol=10) |> noquote()
L8=cbind(M8[,1:3],'|',M8[,4:6],'|',M8[,7:10]) |> noquote() ; L8

RES=rbind(L1,L2,L3,L4,L5,L6,L7,L8)|> noquote()
nrow(RES)
head(RES,30)
tail(RES,30)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/768

849: １３２人目の素数さん [sage] 2025/05/25(日) 06:42:27.34 ID:P4nhnL8B

>>847
このプロトタイプをAIに与えて描画機能やコメントをつけてもらった。

beta.parameter <- function(lower, upper, credMass = 0.95, verbose = FALSE) {

# Helper function to convert decimal numbers to fraction strings using MASS::fractions
fractionStr <- function(x) {
as.character(MASS::fractions(x))
}

# Function to compute beta parameter (beta) based on alpha,
# derived from the condition on the shape of the distribution between lower and upper
f <- function(alpha) {
1 + ((alpha - 1) * log(upper / lower)) / log((1 - lower) / (1 - upper))
}

# Root-finding function: difference between desired credible mass
# and the Beta CDF probability between lower and upper with parameters (alpha, f(alpha))
g <- function(alpha) {
pbeta(upper, alpha, f(alpha)) - pbeta(lower, alpha, f(alpha)) - credMass
}

# Find the root of g(alpha) = 0 over the interval [1, 1e5]
# to find the alpha value that satisfies the credible mass condition
re <- uniroot(g, c(1, 1e5))
alpha <- re$root
beta <- f(alpha)

# Calculate the mean of the Beta distribution
mean <- alpha / (alpha + beta)

# Calculate the mode if defined (alpha > 1 and beta > 1),
# otherwise set mode to NA as it is undefined
mode <- if (alpha > 1 && beta > 1) {
(alpha - 1) / (alpha + beta - 2)
} else {
NA
}

http://rio2016.5ch.net/test/read.cgi/math/1723152147/849

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