高校数学の質問スレ（医者・東大卒専用） Part438 (991ﾚｽ)
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抽出解除 必死ﾁｪｯｶｰ(本家) (べ) 自ID ﾚｽ栞 あぼーん
344: １３２人目の素数さん [sage] 2024/11/30(土)07:28 ID:L4mkprla(1/6)
hex[x_]:=ResourceFunction["HexConvert"][x];
start="100";
end="fff";
d=hex /@ Range[hex[start],hex[end]];
s=StringSplit[#,""]& /@ d;
KaprekarHexQ[x_] := hex[hex@StringJoin@ReverseSort@x - hex@StringJoin@Sort@x] == StringJoin@x;
StringJoin /@ Select[s,KaprekarHexQ]
345: １３２人目の素数さん [sage] 2024/11/30(土)10:21 ID:L4mkprla(2/6)
(* 16進法でｎ桁のカプレカ数を求める *)
n=6
hex[x_]:=ResourceFunction["HexConvert"][x];
s=ResourceFunction["OrderlessCombinations"][hex /@ Range[0,15],{n}];
KaprekarHexQ[x_] := (
d=hex@StringJoin@ReverseSort@x - hex@StringJoin@Sort@x;
lid=StringSplit[hex@d,""];
hex[hex@StringJoin@ReverseSort@lid - hex@StringJoin@Sort@lid]==StringJoin@lid && d!=0
)
re=Select[s,KaprekarHexQ];
hex /@ (hex@StringJoin@ReverseSort@# - hex@StringJoin@Sort@# & /@re) // Union
346: １３２人目の素数さん [sage] 2024/11/30(土)14:45 ID:L4mkprla(3/6)
ｂ進法、ｎ桁のカプレカ数を求めるように拡張
(* ｂ進法でｎ桁のカプレカ数を返す b <= 36 *)
solve[b_,n_]:=(
dec2n[x_] :=(
r=List@Mod[x,b];
q=Floor[x/b];
While[q > 0,PrependTo[r,Mod[q,b]];q=Floor[q/b]];
r
);
DigitsInteger[x_] :=(
le=Length@x;
Table[(Reverse@x)[[i]]*b^(i-1),{i,1,le}]//Total
);
digits=Flatten@{Range[0,9],Alphabet[]};
s=ResourceFunction["OrderlessCombinations"][digits[[Range[1,b]]],{n}];
KaprekarBinQ[x_]:=(
d=DigitsInteger@ReverseSort@x - DigitsInteger@Sort@x;
lid=dec2n[d];
DigitsInteger@ReverseSort@lid - DigitsInteger@Sort@lid == DigitsInteger@lid && d!=0
);
re=Select[s,KaprekarBinQ];
ans10=Union@(DigitsInteger@ReverseSort@# - DigitsInteger@Sort@# & /@ re);
ans2=dec2n /@ ans10;
ans3=Table[digits[[i]],{i,ans2+1}];
Le=Length[ans3];
Table[StringJoin @ (ToString /@ ans3[[i]]),{i,1,Le}]
)
solve[2,10]
solve[16,6]
348: １３２人目の素数さん [sage] 2024/11/30(土)17:54 ID:L4mkprla(4/6)
(*
問題 5桁の疑似ヴァンパイア数を列挙せよ。
*)
f14[n_]:=(
d=IntegerDigits[n];
p=Permutations[d,{5}];
prd=#[[1]]*(1000 #[[2]]+100 #[[3]]+10 #[[4]]+#[[5]])& /@p;
i=Position[prd,n];
ans={};
If[i!={},
idx=i[[1]][[1]];
re=p[[idx]];
AppendTo[ans,{re[[1]],1000re[[2]]+100re[[3]]+10re[[4]]+re[[5]]}]
];
ans
)
res=Partition[Flatten@Table[f14[n],{n,10000,99999}],2];
{#[[1]],#[[2]],#[[1]]#[[2]]} & /@res
349: １３２人目の素数さん [sage] 2024/11/30(土)17:55 ID:L4mkprla(5/6)
{{5, 2051, 10255}, {5, 2105, 10525}, {9, 1251, 11259}, {8, 1481, 11848},
> {6, 2001, 12006}, {6, 2010, 12060}, {3, 4128, 12384}, {5, 2501, 12505},
> {5, 2510, 12550}, {5, 2519, 12595}, {6, 2100, 12600}, {6, 2127, 12762},
> {3, 4281, 12843}, {5, 2591, 12955}, {3, 4515, 13545}, {3, 5001, 15003},
> {3, 5010, 15030}, {6, 2541, 15246}, {3, 5100, 15300}, {3, 5145, 15435},
> {9, 1755, 15795}, {6, 2712, 16272}, {2, 8714, 17428}, {2, 8741, 17482},
> {3, 7125, 21375}, {3, 7251, 21753}, {5, 5021, 25105}, {5, 5102, 25510},
> {9, 3501, 31509}, {9, 3510, 31590}, {8, 4730, 37840}, {8, 4973, 39784},
> {6, 7446, 44676}, {9, 5751, 51759}, {8, 6521, 52168}, {9, 6255, 56295},
> {9, 7461, 67149}, {8, 8600, 68800}, {9, 7911, 71199}, {9, 8775, 78975}}
350(1): １３２人目の素数さん [sage] 2024/11/30(土)17:55 ID:L4mkprla(6/6)
f23[n_]:=(
d=IntegerDigits[n];
p=Permutations[d,{5}];
prd=(10 #[[1]]+#[[2]])(100 #[[3]]+10 #[[4]]+#[[5]])& /@p;
i=Position[prd,n];
ans={};
If[i!={},
idx=i[[1]][[1]];
re=p[[idx]];
AppendTo[ans,{10 re[[1]]+re[[2]],100re[[3]]+10re[[4]]+re[[5]]}]
];
ans
)
res=Partition[Flatten@Table[f23[n],{n,10000,99999}],2];
{{51, 201, 10251}, {26, 401, 10426}, {21, 501, 10521}, {15, 705, 10575},
> {84, 141, 11844}, {60, 201, 12060}, {51, 246, 12546}, {50, 251, 12550},
> {21, 600, 12600}, {14, 926, 12964}, {41, 323, 13243}, {15, 930, 13950},
> {35, 401, 14035}, {41, 350, 14350}, {30, 501, 15030}, {51, 300, 15300},
> {24, 651, 15624}, {75, 231, 17325}, {47, 371, 17437}, {81, 225, 18225},
> {65, 281, 18265}, {87, 210, 18270}, {21, 906, 19026}, {21, 915, 19215},
> {86, 251, 21586}, {27, 810, 21870}, {35, 725, 25375}, {47, 542, 25474},
> {42, 678, 28476}, {32, 926, 29632}, {90, 351, 31590}, {53, 635, 33655},
> {36, 936, 33696}, {63, 585, 36855}, {80, 473, 37840}, {87, 435, 37845},
> {65, 641, 41665}, {89, 482, 42898}, {54, 846, 45684}, {65, 704, 45760},
> {84, 546, 45864}, {57, 834, 47538}, {78, 624, 48672}, {59, 845, 49855},
> {63, 855, 53865}, {65, 875, 56875}, {68, 926, 62968}, {65, 983, 63895},
> {72, 936, 67392}, {75, 906, 67950}, {86, 800, 68800}}
{#[[1]],#[[2]],#[[1]]#[[2]]} & /@res
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