Smallest power of 6 whose decimal expansion contains n: Difference between revisions

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Line 6: =={{header\|11l}}== {{trans\|Python}} <syntaxhighlight lang="11l">F smallest_six(n) V p = BigInt(1) L String(n) !C String(p) p = 6 R p L(n) 22 print(‘#2: #.’.format(n, smallest_six(n)))</syntaxhighlight> {{out}} <pre> 0: 10077696 1: 1 2: 216 3: 36 4: 46656 5: 46656 6: 6 7: 7776 8: 2176782336 9: 1296 10: 10077696 11: 2821109907456 12: 1296 13: 13060694016 14: 6140942214464815497216 15: 101559956668416 16: 216 17: 60466176 18: 470184984576 19: 21936950640377856 20: 170581728179578208256 21: 216 </pre> =={{header\|ALGOL 68}}== {{works with\|ALGOL 68G\|Any - tested with release 2.8.3.win32}} Uses ALGOL 68G's LONG LONG INT large integers, the default precision is sufficient for this task. Also uses the ALGOL 68G specific string in string procedure. <~~lang~~syntaxhighlight lang="algol68">BEGIN # find the smallest k such that the decimal representation of 6^k contains n for 0 <= n <= 21 # # returns s blank-padded on the right to at least len characters # PROC right pad = ( STRING s, INT len )STRING: Line 60 ⟶ 98: OD OD END</~~lang~~syntaxhighlight> {{out}} <pre> Line 85 ⟶ 123: 20: 6^26 170 581 728 179 578 208 256 21: 6^3 216 </pre> =={{header\|ALGOL W}}== Algol W doesn't have integers larger than 32 bits, however we can handle the required numbers with arrays of digits. <syntaxhighlight lang="algolw">begin % find the smallest power of 6 that contains n for 0 <= n <= 21 % % we assume that powers of 6 upto 6^32 will be sufficient % % as Algol W does not have integers longer than 32 bits, the powers % % will be held in an array where each element is a single digit of the % % power, the least significant digit of 6^n is in powers( n, 1 ) % integer array powers ( 0 :: 32, 1 :: 32 ); % the powers % integer array digits ( 0 :: 32 ); % the number of digits in each power % integer array lowest ( 0 :: 21 ); % the lowest power containing the idx % for n := 0 until 21 do lowest( n ) := -1; % 6^0 = 1, which is the lowest power containing 1 % lowest( 1 ) := 0; powers( 0, 1 ) := 1; for d := 2 until 32 do powers( 0, d ) := 0; digits( 0 ) := 1; % calculate the remaining powers and find the numbers 0..21 % for p := 1 until 32 do begin integer carry, dPos, dMax; dPos := 1; dMax := digits( p - 1 ); carry := 0; % compute the power p and find the single digit numbers % while dPos <= dMax do begin integer d; d := carry + ( powers( p - 1, dPos ) 6 ); carry := d div 10; d := d rem 10; if lowest( d ) < 0 then lowest( d ) := p; powers( p, dPos ) := d; dPos := dPos + 1 end while_dPos_le_dMax ; if carry = 0 then digits( p ) := dMax else begin % the power p has one more digit than the previous % digits( p ) := dPos; powers( p, dPos ) := carry; if lowest( carry ) < 0 then lowest( carry ) := p; end if_carry_eq_0__ ; % find the two digit numbers % for n := 10 until 21 do begin if lowest( n ) < 0 then begin integer h, l; h := n div 10; l := n rem 10; for d := digits( p ) - 1 step -1 until 1 do begin if powers( p, d ) = l and powers( p, d + 1 ) = h then lowest( n ) := p end for_d end if_lowest_n_lt_0 end for_n end for_p ; % show the lowest powers that contain the numbers 0..21 % for n := 0 until 21 do begin integer p; p := lowest( n ); write( i_w := 2, s_w := 0, n, " in 6^", p, ": " ); for d := digits( p ) step -1 until 1 do writeon( i_w := 1, s_w := 0, powers( p, d ) ) end for_n end.</syntaxhighlight> {{out}} <pre> 0 in 6^ 9: 10077696 1 in 6^ 0: 1 2 in 6^ 3: 216 3 in 6^ 2: 36 4 in 6^ 6: 46656 5 in 6^ 6: 46656 6 in 6^ 1: 6 7 in 6^ 5: 7776 8 in 6^12: 2176782336 9 in 6^ 4: 1296 10 in 6^ 9: 10077696 11 in 6^16: 2821109907456 12 in 6^ 4: 1296 13 in 6^13: 13060694016 14 in 6^28: 6140942214464815497216 15 in 6^18: 101559956668416 16 in 6^ 3: 216 17 in 6^10: 60466176 18 in 6^15: 470184984576 19 in 6^21: 21936950640377856 20 in 6^26: 170581728179578208256 21 in 6^ 3: 216 </pre> =={{header\|Arturo}}== <syntaxhighlight lang="arturo">loop 0..22 'n [ ns: to :string n print [pad to :string n 2 "->" 6 ^ first select.first 0..∞ 'x -> contains? to :string 6^x ns] ]</syntaxhighlight> {{out}} <pre> 0 -> 10077696 1 -> 1 2 -> 216 3 -> 36 4 -> 46656 5 -> 46656 6 -> 6 7 -> 7776 8 -> 2176782336 9 -> 1296 10 -> 10077696 11 -> 2821109907456 12 -> 1296 13 -> 13060694016 14 -> 6140942214464815497216 15 -> 101559956668416 16 -> 216 17 -> 60466176 18 -> 470184984576 19 -> 21936950640377856 20 -> 170581728179578208256 21 -> 216 22 -> 131621703842267136</pre> =={{header\|AWK}}== <syntaxhighlight lang="awk"> # syntax: GAWK -f SMALLEST_POWER_OF_6_WHOSE_DECIMAL_EXPANSION_CONTAINS_N.AWK BEGIN { printf(" n power %30s\n","smallest power of 6") for (n=0; n<22; n++) { p = 1 power = 0 while (p !~ n) { p = 6 power++ } printf("%2d %5d %'30d\n",n,power,p) } exit(0) } </syntaxhighlight> {{out}} <pre> n power smallest power of 6 0 9 10,077,696 1 0 1 2 3 216 3 2 36 4 6 46,656 5 6 46,656 6 1 6 7 5 7,776 8 12 2,176,782,336 9 4 1,296 10 9 10,077,696 11 16 2,821,109,907,456 12 4 1,296 13 13 13,060,694,016 14 28 6,140,942,214,464,815,497,216 15 18 101,559,956,668,416 16 3 216 17 10 60,466,176 18 15 470,184,984,576 19 21 21,936,950,640,377,856 20 26 170,581,728,179,578,208,256 21 3 216 </pre> =={{header\|C}}== <~~lang~~syntaxhighlight Clang="c">#include <stdio.h> #include <string.h> #include <gmp.h> Line 121 ⟶ 322: return 0; }</~~lang~~syntaxhighlight> {{out}} Line 149 ⟶ 350: =={{header\|C++}}== <~~lang~~syntaxhighlight lang="cpp">#include <iostream> #include <iomanip> #include <string> Line 171 ⟶ 372: } return 0; }</~~lang~~syntaxhighlight> {{out}} Line 196 ⟶ 397: 20: 170581728179578208256 21: 216</pre> =={{header\|CLU}}== <syntaxhighlight lang="clu">% This program uses the bigint type that comes with PCLU. % It is in "misc.lib" % % pclu -merge $CLUHOME/lib/misc.lib -compile n6_contains_6.clu smallest_power_6 = proc (n: int) returns (int, bigint) n_str: string := int$unparse(n) six_power: bigint := bigint$i2bi(1) six: bigint := bigint$i2bi(6) n_power: int := 0 while true do pow_str: string := bigint$unparse(six_power) if string$indexs(n_str, pow_str) ~= 0 then return(n_power, six_power) end six_power := six_power six n_power := n_power + 1 end end smallest_power_6 start_up = proc () po: stream := stream$primary_output() for n: int in int$from_to(0, 21) do p: int val: bigint stream$putright(po, int$unparse(n), 2) stream$puts(po, ": 6^") p, val := smallest_power_6(n) stream$putleft(po, int$unparse(p), 2) stream$puts(po, " = ") stream$putright(po, bigint$unparse(val), 30) stream$putl(po, "") end end start_up</syntaxhighlight> {{out}} <pre> 0: 6^9 = 10077696 1: 6^0 = 1 2: 6^3 = 216 3: 6^2 = 36 4: 6^6 = 46656 5: 6^6 = 46656 6: 6^1 = 6 7: 6^5 = 7776 8: 6^12 = 2176782336 9: 6^4 = 1296 10: 6^9 = 10077696 11: 6^16 = 2821109907456 12: 6^4 = 1296 13: 6^13 = 13060694016 14: 6^28 = 6140942214464815497216 15: 6^18 = 101559956668416 16: 6^3 = 216 17: 6^10 = 60466176 18: 6^15 = 470184984576 19: 6^21 = 21936950640377856 20: 6^26 = 170581728179578208256 21: 6^3 = 216</pre> =={{header\|F_Sharp\|F#}}== <~~lang~~syntaxhighlight lang="fsharp"> // Nigel Galloway. April 9th., 2021 let rec fN i g e l=match l%i=g,l/10I with (true,_)->e \|(_,l) when l=0I->fN i g (e6I) (e6I) \|(_,l)->fN i g e l [0I..99I]\|>Seq.iter(fun n->printfn "%2d %A" (int n)(fN(if n>9I then 100I else 10I) n 1I 1I)) </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 310 ⟶ 571: =={{header\|Factor}}== {{works with\|Factor\|0.99 2021-02-05}} <~~lang~~syntaxhighlight lang="factor">USING: formatting kernel lists lists.lazy math math.functions present sequences tools.memory.private ; Line 319 ⟶ 580: present powers-of-6 [ present subseq? ] with lfilter car ; 22 [ dup smallest commas "%2d %s\n" printf ] each-integer</~~lang~~syntaxhighlight> {{out}} <pre> Line 344 ⟶ 605: 20 170,581,728,179,578,208,256 21 216 </pre> =={{header\|FreeBASIC}}== {{trans\|Ring}} <syntaxhighlight lang="freebasic"> Print !"\ntrabajando...\n" Print !"M¡nima potencia de 6 cuya expansi¢n decimal contiene n:\n" Dim As Uinteger num = 0, limit = 200, m For n As Ubyte = 0 To 21 Dim As String strn = Str(n) For m = 0 To limit Dim As String strpow = Str(6 ^ m) Dim As Ulong ind = Instr(strpow,strn) If ind > 0 Then Print Using "##. 6^\\ = &"; n; Str(m); strpow Exit For End If Next m Next n Print !"\n--- terminado, pulsa RETURN---" Sleep </syntaxhighlight> =={{header\|Go}}== {{trans\|Wren}} <syntaxhighlight lang="go">package main import ( "fmt" "math/big" "strconv" "strings" ) // Adds thousand separators to an integral string. func commatize(s string) string { neg := false if strings.HasPrefix(s, "-") { s = s[1:] neg = true } le := len(s) for i := le - 3; i >= 1; i -= 3 { s = s[0:i] + "," + s[i:] } if !neg { return s } return "-" + s } func main() { fmt.Println(" n smallest power of 6 which contains n") six := big.NewInt(6) for n := 0; n <= 21; n++ { ns := strconv.Itoa(n) i := int64(0) for { bi := big.NewInt(i) pow6 := bi.Exp(six, bi, nil).String() if strings.Contains(pow6, ns) { fmt.Printf("%2d 6^%-2d = %s\n", n, i, commatize(pow6)) break } i++ } } }</syntaxhighlight> {{out}} <pre> n smallest power of 6 which contains n 0 6^9 = 10,077,696 1 6^0 = 1 2 6^3 = 216 3 6^2 = 36 4 6^6 = 46,656 5 6^6 = 46,656 6 6^1 = 6 7 6^5 = 7,776 8 6^12 = 2,176,782,336 9 6^4 = 1,296 10 6^9 = 10,077,696 11 6^16 = 2,821,109,907,456 12 6^4 = 1,296 13 6^13 = 13,060,694,016 14 6^28 = 6,140,942,214,464,815,497,216 15 6^18 = 101,559,956,668,416 16 6^3 = 216 17 6^10 = 60,466,176 18 6^15 = 470,184,984,576 19 6^21 = 21,936,950,640,377,856 20 6^26 = 170,581,728,179,578,208,256 21 6^3 = 216 </pre> =={{header\|Haskell}}== <~~lang~~syntaxhighlight lang="haskell">import Data.List (find, isInfixOf) import Text.Printf (printf) smallest :: Integer -> Integer smallest n = d where Just d = find ((show n `isInfixOf`) . show) sixes sixes :: [Integer] sixes = iterate (* 6) 1 ~~smallest :: Integer -> Integer~~ ~~smallest n =~~ ~~head $~~ ~~filter~~ ~~((show n `isInfixOf`) . show)~~ ~~sixes~~ main :: IO () main = putStr $ [0 .. 21] >>= printf "%2d: %d\n" <> smallest</syntaxhighlight> ~~concatMap~~ ~~(printf "%2d: %d\n" <> smallest)~~ ~~[0 .. 21]</lang>~~ {{out}} <pre> 0: 10077696 1: 1 Line 391 ⟶ 745: 20: 170581728179578208256 21: 216</pre> =={{header\|jq}}== '''Works with gojq, the Go implementation of jq''' gojq provides unbounded-precision integer arithmetic and is therefore appropriate for this task. <syntaxhighlight lang="jq"># To preserve precision: def power($b): . as $in \| reduce range(0;$b) as $i (1; . * $in); range(0;22) \| . as $in \| tostring as $n \| first(range(0;infinite) as $i \| 6 \| power($i) \| . as $p \| tostring \| (index($n) // empty) \| [$in,$i,$p] )</syntaxhighlight> {{out}} <pre> [0,9,10077696] [1,0,1] [2,3,216] [3,2,36] [4,6,46656] [5,6,46656] [6,1,6] [7,5,7776] [8,12,2176782336] [9,4,1296] [10,9,10077696] [11,16,2821109907456] [12,4,1296] [13,13,13060694016] [14,28,6140942214464815497216] [15,18,101559956668416] [16,3,216] [17,10,60466176] [18,15,470184984576] [19,21,21936950640377856] [20,26,170581728179578208256] [21,3,216] </pre> =={{header\|Julia}}== <~~lang~~syntaxhighlight lang="julia">using Formatting digcontains(n, dig) = contains(String(Char.(digits(n))), String(Char.(dig))) Line 409 ⟶ 802: println(rpad(n, 5), format(findpow6containing(n), commas=true)) end </~~lang~~syntaxhighlight>{{out}} <pre> 0 10,077,696 Line 434 ⟶ 827: 21 216 </pre> =={{header\|Mathematica}}/{{header\|Wolfram Language}}== <syntaxhighlight lang="mathematica">ClearAll[SmallestPowerContainingN] SmallestPowerContainingN[n_Integer] := Module[{i = 1, test}, While[True, test = 6^i; If[SequenceCount[IntegerDigits[test], IntegerDigits[n]] > 0, Return[{n, i, test}]]; i++; ] ] Grid[SmallestPowerContainingN /@ Range[0, 21]]</syntaxhighlight> {{out}} <pre>0 9 10077696 1 3 216 2 3 216 3 2 36 4 6 46656 5 6 46656 6 1 6 7 5 7776 8 12 2176782336 9 4 1296 10 9 10077696 11 16 2821109907456 12 4 1296 13 13 13060694016 14 28 6140942214464815497216 15 18 101559956668416 16 3 216 17 10 60466176 18 15 470184984576 19 21 21936950640377856 20 26 170581728179578208256 21 3 216</pre> =={{header\|Nim}}== {{libheader\|bignum}} <syntaxhighlight lang="nim">import strformat, strutils import bignum var toFind = {0..21} var results: array[0..21, (int, string)] var p = newInt(1) var k = 0 while toFind.card > 0: let str = $p for n in toFind: if str.find($n) >= 0: results[n] = (k, str) toFind.excl(n) p = 6 inc k echo "Smallest values of k such that 6^k contains n:" for n, (k, s) in results: echo &"{n:2}: 6^{k:<2} = {s}"</syntaxhighlight> {{out}} <pre>Smallest values of k such that 6^k contains n: 0: 6^9 = 10077696 1: 6^0 = 1 2: 6^3 = 216 3: 6^2 = 36 4: 6^6 = 46656 5: 6^6 = 46656 6: 6^1 = 6 7: 6^5 = 7776 8: 6^12 = 2176782336 9: 6^4 = 1296 10: 6^9 = 10077696 11: 6^16 = 2821109907456 12: 6^4 = 1296 13: 6^13 = 13060694016 14: 6^28 = 6140942214464815497216 15: 6^18 = 101559956668416 16: 6^3 = 216 17: 6^10 = 60466176 18: 6^15 = 470184984576 19: 6^21 = 21936950640377856 20: 6^26 = 170581728179578208256 21: 6^3 = 216</pre> =={{header\|Pascal}}== ==={{~~Works with~~header\|Free Pascal}}=== Doing long multiplikation like in primorial task.<BR>I used to check every numberstring one after the other on one 6^ n string.Gets really slow on high n<BR>After a closer look into [[Phix\|Smallest_power_of_6_whose_decimal_expansion_contains_n#Phix]] I applied a slghtly modified version of Pete~~, to get down < 10 secs on my 2200G for DIGITS = 7.TIO.RUN is slower~~. <~~lang~~syntaxhighlight lang="pascal">program PotOf6; //First occurence of a numberstring with max decimal DIGTIS digits in 6^n {$IFDEF FPC} {$MODE DELPHI} {$Optimization ON,ALL} {$COPERATORS ON}{$CODEALIGN proc=16} {$ENDIF} ~~{$Optimization ON,ALL}~~ {$IFDEF WINDOWS} ~~{$ELSE}~~ {$APPTYPE CONSOLE} {$ENDIF} Line 450 ⟶ 925: sysutils; const //decimal places used by multiplication and for string conversion ~~POT_LIMIT = 70000;~~ { ~~DIGITS~~ calcDigits = 8; PowerBase = 6; // don't use 10^n ;-) ~~67584 99999998 46238296~~ ~~Max power 68479~~ // for PowerBase = 2 maxvalues for POT_LIMIT and STRCOUNT ~~Found: 100000000 Time used 148.584 secs}~~ // DIGITS = 8;decLimit= 10010001000;POT_LIMIT = 114715;STRCOUNT = 83789; ~~DIGITS = 7;~~ DIGITS = 7;decLimit= 1010001000;POT_LIMIT = 32804;STRCOUNT = 24960; // DIGITS = 6;decLimit= 10001000;POT_LIMIT = 9112;STRCOUNT = 7348; // DIGITS = 5;decLimit= 1001000;POT_LIMIT = 2750;STRCOUNT = 2148; // DIGITS = 4;decLimit= 101000;POT_LIMIT = 809;STRCOUNT = 616; // DIGITS = 3;decLimit= 1000;POT_LIMIT = 215;STRCOUNT = 175; // DIGITS = 2;decLimit= 100;POT_LIMIT = 66;STRCOUNT = 45; type tMulElem = Uint32; Line 463 ⟶ 945: tFound = record foundIndex~~: Uint32;~~, ~~foundStr~~foundStrIdx :~~Ansistring~~ Uint32; end; var {$ALIGN 32} PotArrN : tPotArrN; StrDec4Dgts : array[0..9999] of String[4]; Str_Found : array of tFound; FoundString : array of AnsiString; CheckedNum : array of boolean; Pot_N_str : AnsiString; FirstMissing, ~~Str_Found : array of tFound;~~ ~~FirstMissing~~FoundIdx :NativeInt; T0 : INt64; procedure ~~Init_Mul(number:NativeInt)~~Init_StrDec4Dgts; var ~~MaxMulIdx~~s : ~~NativeInt~~string[4]; i : integer; ~~Begin~~ a,b,c,d : char; ~~MaxMulIdx := trunc(POT_LIMITln(number)/ln(10)/9+2);~~ ~~setlength(PotArrN[0],MaxMulIdx);~~ ~~setlength(PotArrN[1],MaxMulIdx);~~ ~~PotArrN[0,0] := 1;~~ ~~end;~~ ~~function Mul_N(var Mul1,Mul2:tMul;limit,n:Uint32):NativeInt;~~ ~~//Mul2 = nMul1. n must be < LongWordDec !~~ ~~const~~ ~~LongWordDec = 100010001000;~~ ~~var~~ ~~pM1,pM2 : tpMul;~~ ~~carry,prod : Uint64;~~ begin ~~pM1~~i := ~~@Mul1[~~0]; ~~pM2~~s := ~~@Mul2[0]~~'0000'; ~~carry~~For a := '0;' to '9' do Begin ~~result :=0;~~ s[1] := a; ~~repeat~~ ~~prod~~For b := ~~npM1[result]+Carry;~~'0' to '9' do begin ~~Carry := prod Div LongWordDec;~~ ~~pM2~~ s[~~result~~2] := ~~Prod - CarryLongWordDec~~b; For c := '0' to '9' do ~~inc(result);~~ ~~until~~ ~~result~~ > ~~limit;~~ begin IF ~~Carry~~ <> 0 ~~then~~ s[3] := c; ~~pM2[result]~~ For d := ~~Carry~~'0' to '9' do begin ~~else~~ ~~dec(result)~~ s[4] := d; StrDec4Dgts[i]:= s; inc(i); end; end; end; end; end; Line 520 ⟶ 1,000: exit; end; toIdx := 4(toIdx DIV 3)+toIdx MOD 3 +1 ; ~~inc(toIdx);~~ setlength(result,toIdx); repeat result[toIdx] := s[FromIdx]; result[toIdx-1] := s[FromIdx-1]; result[toIdx-2] := s[FromIdx-2]; Line 537 ⟶ 1,016: dec(fromIdx); end; end; procedure Init_Mul(number:NativeInt); var dgtCount, MaxMulIdx : NativeInt; Begin dgtCount := trunc(POT_LIMITln(number)/ln(10))+1; MaxMulIdx := dgtCount DIV calcDigits +2; setlength(PotArrN[0],MaxMulIdx); setlength(PotArrN[1],MaxMulIdx); PotArrN[0,0] := 1; setlength(Pot_N_str,dgtCount); end; function Mul_PowerBase(var Mul1,Mul2:tMul;limit:Uint32):NativeInt; //Mul2 = nMul1. n must be < LongWordDec ! const LongWordDec = 10010001000; var pM1,pM2 : tpMul; carry,prod : Uint64; begin pM1 := @Mul1[0]; pM2 := @Mul2[0]; carry := 0; result :=0; repeat prod := PowerBasepM1[result]+Carry; Carry := prod Div LongWordDec; pM2[result] := Prod - CarryLongWordDec; inc(result); until result > limit; IF Carry <> 0 then pM2[result] := Carry else dec(result); end; procedure ConvToStr(var s:Ansistring;const Mul:tMul;i:NativeInt); var s9s8: string[9calcDigits]; pS : pChar; j,k,d,m : NativeInt; begin // ij := ~~High~~(~~MUL~~i+1)calcDigits; ~~j := (i+1)9;~~ setlength(s,j+1); pS := ~~pChar(~~@s)[1]; m := Mul[i]; ~~// fill complete with '0'~~ ~~fillchar~~str(pSMul[0i],~~j,'0'~~s8); j := length(s8); ~~str(Mul[i],S9);~~ move(s8[1],pS[0],j); ~~j := length(s9);~~ ~~move(s9[1],pS[0],j);~~ k := j; dec(i); If i >= 0 then repeat ~~str(Mul~~m := MUL[i]~~,S9)~~;~~// no leading '0'~~ jd := ~~length(s9)~~m div 10000; ~~inc(k,9)~~m := m-10000d; move(StrDec4Dgts[d][1],pS[k],4); ~~//move to the right place, leading '0' is already there~~ move(s9StrDec4Dgts[m][1],pS[k-j+4],j4); inc(k,calcDigits); dec(i); until i<0; Line 569 ⟶ 1,084: function CheckOneString(const s:Ansistring;pow:NativeInt):NativeInt; //check every possible number from one to DIGITS digits, //if it is still missing in the list var pChecked : pBoolean; i,k,lmt,num : NativeInt; csoneFound : ~~Ansistring~~boolean; begin pChecked := @CheckedNum[0]; result := 0; csoneFound := ''false; lmt := length(s); For i := 1 to lmt do Line 584 ⟶ 1,101: repeat num := num10+ Ord(s[k])-Ord('0'); IF (num >= FirstMissing) AND Not(~~str_Found~~pChecked[num]~~.foundIndex = 0~~) then begin //memorize that string commatized ~~str_Found[num].foundIndex:= pow+1;~~ if NOT(oneFound) then ~~// commatize only once. reference counted string~~ ~~if cs ='' then~~Begin csoneFound := ~~Commatize(s)~~true; ~~str_Found~~ FoundString[~~num~~FoundIDX]~~.foundStr~~ := csCommatize(s); FoundIDX += 1; end; pChecked[num]:= true; with str_Found[num] do Begin foundIndex:= pow+1; foundStrIdx:= FoundIDX-1; end; inc(result); if num =~~irstMissing~~FirstMissing then repeat ~~while str_Found[FirstMissing].foundIndex <> 0 do~~ inc(FirstMissing); until str_Found[FirstMissing].foundIndex =0; end; inc(k) Line 602 ⟶ 1,128: var i,j,~~number~~k,toggle,MaxMulIdx,found~~,decLimit~~: Int32; Begin T0 := GetTickCount64; ~~number := 6;//<1e9 no power of 10 ;-)~~ ~~decLimit := 1;~~ ~~For i := 1 to digits do~~ ~~decLimit = 10;~~ setlength(Str_Found,decLimit); setlength(CheckedNum,decLimit); ~~Init_Mul(number);~~ setlength(FoundString,STRCOUNT); FirstMissing := 0; FoundIdx := 0; Init_StrDec4Dgts; Init_Mul(PowerBase); writeln('Init in ',(GetTickCount64-T0)/1000:8:3,' secs'); T0 := GetTickCount64; toggle := 0; found := 0; ~~FirstMissing := 0;~~ MaxMulIdx := 0; k := 0; For j := 0 to POT_LIMIT do Begin // if j MOD 20 = 0 then writeln; ConvToStr(Pot_N_str,PotArrN[toggle],MaxMulIdx); ~~inc(found,~~i := CheckOneString(Pot_N_str,j)); found += i; ~~MaxMulIdx := Mul_N(PotArrN[toggle],PotArrN[1-toggle],MaxMulIdx,number);~~ if i <> 0 then k += 1; MaxMulIdx := Mul_PowerBase(PotArrN[toggle],PotArrN[1-toggle],MaxMulIdx); toggle := 1-toggle; ~~if found>=decLimit then~~ if FirstMissing = decLimit then Begin writeln(#10,'Max power ',j,' with ',length(Pot_N_str),' digits'); break; end; // if (j and 1023) = 0 then write(#13,j:10,found:10,FirstMissing:10); ~~write(j:10,found:10,firstMissing:10,#13);~~ end; writeln(#13#10,'Found: ',found,' in ',k,' strings. Time used ',(GetTickCount64-T0)/1000:8:3,' secs'); ~~writeln(#10,'Found: ',found,' Time used ',(GetTickCount64-T0)/1000:8:3,' secs');~~ For i := 0 to 22 do//decLimit-1 do with Str_Found[i] do writeln(i:10,' ',PowerBase,'^',foundIndex-1:5,' ',(FoundString[foundStrIdx]):30); ~~if foundIndex >0 then~~ end. ~~writeln(i:10,' ',number,'^',foundIndex-1:5,' ',foundStr);~~ </syntaxhighlight> ~~readln;~~ {{out\|@TIO.RUN}} ~~end.</lang>~~ ~~{{out}}~~ <pre> Init in 0.062 secs ~~TIO.RUN output~~ ~~//Power found first missing~~ ~~0 1 0~~ ~~1024 751817 10020~~ ~~2048 2168981 100017~~ ~~3072 3733971 100017~~ ~~4096 5305316 100672~~ ~~5120 6747391 104835~~ ~~6144 7922626 575115~~ ~~7168 8776137 1000007~~ ~~8192 9336696 1000015~~ ~~9216 9667898 1000020~~ ~~10240 9846933 1000088~~ ~~11264 9935108 1000135~~ ~~12288 9974783 1000204~~ ~~13312 9990953 1000204~~ ~~14336 9997035 1000204~~ ~~15360 9999102 1000204~~ ~~16384 9999744 1029358~~ ~~17408 9999934 1029358~~ ~~18432 9999978 1029358~~ ~~19456 9999997 8091358~~ ~~20480 9999999 8091358~~ ~~21504 9999999 8091358~~ ~~Max power 21798~~ Max power 21798 with 16963 digits ~~Found: 10000000 Time used 14.882 secs~~ ~~0 6^ 9 10,077,696~~ ~~1 6^ 0 1~~ ~~2 6^ 3 216~~ ~~3 6^ 2 36~~ ~~4 6^ 6 46,656~~ ~~5 6^ 6 46,656~~ ~~6 6^ 1 6~~ ~~7 6^ 5 7,776~~ ~~8 6^ 12 2,176,782,336~~ ~~9 6^ 4 1,296~~ ~~10 6^ 9 10,077,696~~ ~~11 6^ 16 2,821,109,907,456~~ ~~12 6^ 4 1,296~~ ~~13 6^ 13 13,060,694,016~~ ~~14 6^ 28 6,140,942,214,464,815,497,216~~ ~~15 6^ 18 101,559,956,668,416~~ ~~16 6^ 3 216~~ ~~17 6^ 10 60,466,176~~ ~~18 6^ 15 470,184,984,576~~ ~~19 6^ 21 21,936,950,640,377,856~~ ~~20 6^ 26 170,581,728,179,578,208,256~~ ~~21 6^ 3 216~~ ~~22 6^ 22 131,621,703,842,267,136~~ Found: 10000000 in 15889 strings. Time used 8.114 secs ~~Real time: 15.373 s~~ ~~User time: 14.953 s~~ 0 6^ 9 10,077,696 ~~Sys. time: 0.254 s~~ 1 6^ 0 1 ~~CPU share: 98.92 %</pre>~~ 2 6^ 3 216 3 6^ 2 36 4 6^ 6 46,656 5 6^ 6 46,656 6 6^ 1 6 7 6^ 5 7,776 8 6^ 12 2,176,782,336 9 6^ 4 1,296 10 6^ 9 10,077,696 11 6^ 16 2,821,109,907,456 12 6^ 4 1,296 13 6^ 13 13,060,694,016 14 6^ 28 6,140,942,214,464,815,497,216 15 6^ 18 101,559,956,668,416 16 6^ 3 216 17 6^ 10 60,466,176 18 6^ 15 470,184,984,576 19 6^ 21 21,936,950,640,377,856 20 6^ 26 170,581,728,179,578,208,256 21 6^ 3 216 22 6^ 22 131,621,703,842,267,136 Real time: 8.383 s User time: 8.133 s Sys. time: 0.185 s CPU share: 99.23 % </pre> =={{header\|Perl}}== <~~lang~~syntaxhighlight lang="perl">use strict; use warnings; use List::Util 'first'; Line 707 ⟶ 1,214: my $e = first { 6$_ =~ /$n/ } 0..1000; printf "%7d: 6^%-3s %s\n", $n, $e, comma 6$e; }</~~lang~~syntaxhighlight> {{out}} <pre> 0: 6^9 10,077,696 Line 737 ⟶ 1,244: (Related recent task: [[Show_the_(decimal)_value_of_a_number_of_1s_appended_with_a_3,_then_squared#Phix]]) <!--<~~lang~~syntaxhighlight ~~Phix~~lang="phix">(phixonline)--> <span style="color: #008080;">constant</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">22</span> <span style="color: #000080;font-style:italic;">-- (tested to 10,000,000)</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">(),</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t0</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> Line 783 ⟶ 1,290: <span style="color: #008080;">end</span> <span style="color: #008080;">while</span> <span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">printf</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"%2d %29s = 6^%d\n"</span><span style="color: #0000FF;">},</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pwr</span><span style="color: #0000FF;">}),</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)})</span> <!--</~~lang~~syntaxhighlight>--> {{out}} Line 813 ⟶ 1,320: =={{header\|Python}}== <~~lang~~syntaxhighlight lang="python">def smallest_six(n): p = 1 while str(n) not in str(p): p = 6 Line 819 ⟶ 1,326: for n in range(22): print("{:2}: {}".format(n, smallest_six(n)))</~~lang~~syntaxhighlight> {{out}} <pre> 0: 10077696 Line 844 ⟶ 1,351: 21: 216</pre> =={{header\|~~Raku~~Quackery}}== <syntaxhighlight lang="Quackery"> [ 0 swap ~~<lang perl6>use Lingua::EN::Numbers;~~ [ dip 1+ 10 / dup 0 = until ] drop ] is digits ( n --> n ) [ 10 over digits * temp put false unrot [ over temp share mod over = iff [ rot not unrot ] done dip [ 10 / ] over 0 = until ] 2drop temp release ] is contains ( n n --> b ) [ -1 swap [ dip 1+ over 6 swap over contains until ] drop ] is smallest ( n --> n ) 22 times [ i^ 10 < if sp i^ echo say " --> " 6 i^ smallest echo cr ] cr say "The smallest power of 6 whose decimal expansion contains 31415926 is 6^" 31415926 smallest echo say "." cr</syntaxhighlight> {{out}} <pre> 0 --> 10077696 1 --> 1 2 --> 216 3 --> 36 4 --> 46656 5 --> 46656 6 --> 6 7 --> 7776 8 --> 2176782336 9 --> 1296 10 --> 10077696 11 --> 2821109907456 12 --> 1296 13 --> 13060694016 14 --> 6140942214464815497216 15 --> 101559956668416 16 --> 216 17 --> 60466176 18 --> 470184984576 19 --> 21936950640377856 20 --> 170581728179578208256 21 --> 216 The smallest power of 6 whose decimal expansion contains 31415926 is 6^4261.</pre> =={{header\|Raku}}== <syntaxhighlight lang="raku" line>use Lingua::EN::Numbers; ~~sub super ($n) { $n.trans(<0 1 2 3 4 5 6 7 8 9> => <⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹>) }~~ my @po6 = ^Inf .map: .exp: 6; Line 855 ⟶ 1,424: sprintf "%3d: 6%-4s %s", $n, .&super, comma @po6[$_] given @po6.first: .contains($n), :k };</~~lang~~syntaxhighlight> {{out}} <pre> 0: 6⁹ 10,077,696 Line 882 ⟶ 1,451: =={{header\|REXX}}== <~~lang~~syntaxhighlight lang="rexx">/REXX pgm finds the smallest (decimal) power of 6 which contains N, where N < 22. / numeric digits 100 /ensure enough decimal digs for 6N / parse arg hi . /obtain optional argument from the CL./ Line 903 ⟶ 1,472: exit 0 /stick a fork in it, we're all done. / /──────────────────────────────────────────────────────────────────────────────────────/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</~~lang~~syntaxhighlight> {{out\|output\|text=  when using the default input:}} <pre> Line 934 ⟶ 1,503: =={{header\|Ring}}== <~~lang~~syntaxhighlight lang="ring"> load "stdlib.ring" Line 957 ⟶ 1,526: see "done..." + nl </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 987 ⟶ 1,556: </pre> =={{header\|RPL}}== 1980s RPL can only handle 64-bit unsigned integers, which means a multi-precision multiplication is here required. {{works with\|Halcyon Calc\|4.2.7}} {\| class="wikitable" ! RPL code ! Comment \|- \| ≪ 1000000000 → x n p ≪ { } # 0d x SIZE 1 '''FOR''' j x j GET n * + DUP p / SWAP OVER p * - ROT + SWAP -1 '''STEP''' '''IF''' DUP # 0d ≠ '''THEN''' SWAP + '''ELSE''' DROP '''END''' ≫ ≫ '<span style="color:blue">MMULT</span>' STO ≪ "" SWAP 1 OVER SIZE '''FOR''' d DUP d GET →STR 3 OVER SIZE 1 - SUB '''IF''' d 1 ≠ '''THEN''' '''WHILE''' DUP SIZE 9 < REPEAT "0" SWAP + '''END END''' ROT SWAP + SWAP '''NEXT''' DROP ≫ '<span style="color:blue">M→STR</span>' STO ≪ { # 1d } SWAP WHILE DUP REPEAT SWAP 6 <span style="color:blue">MMULT</span> SWAP 1 - END DROP <span style="color:blue">M→STR</span> ≫ '<span style="color:blue">POW6</span>' STO ≪ DEC { } 0 21 '''FOR''' n n →STR -1 DO 1 + DUP '''POW6''' '''UNTIL''' 3 PICK POS '''END''' <span style="color:blue">POW6</span> ROT SWAP + SWAP DROP NEXT ≫ '<span style="color:blue">TASK</span>' STO \| <span style="color:blue">MMULT</span> ''( { #multi #precision } n -- { #multi #precision } )'' initialize stack with empty result number and carry loop from the lowest digit block multiply block by n, add carry prepare carry for next block if carry ≠ 0 then add it as a new block <span style="color:blue">M→STR</span> ''( { #multi #precision } -- "integer" )'' for each digit block turn it into string, remove both ends if not the highest block fill with "0" add to previous blocks' string <span style="color:blue">POW6</span> ''( n -- { #multi #precision } )'' { #1d } is 1 in multi-precision multiply n times by 6 make it a string Forces decimal mode for integer display for n < 22 turn n into string, initialize counter get 6^n until "n" in "6^n" remake n a string and add it to result list \|} {{out}} <pre> 1: { "10077696" "1" "216" "36" "46656" "46656" "6" "7776" "2176782336" "1296" "10077696" "2821109907456" "1296" "13060694016" "6140942214464815497216" "101559956668416" "216" "60466176" "470184984576" "21936950640377856" "170581728179578208256" "216" } </pre> ====2000s RPL version==== Big integers are native in this version. {{works with\|HP\|49}} ≪ { } 0 21 '''FOR''' n 0 '''WHILE''' 6 OVER ^ →STR n →STR POS NOT '''REPEAT''' 1 + '''END''' "'6^" SWAP + STR→ + '''NEXT''' ≫ '<span style="color:blue">TASK</span>' STO {{out}} <pre> 1: { 6^9 6^0 6^3 6^2 6^6 6^6 6^1 6^5 6^12 6^4 6^9 6^16 6^4 6^13 6^28 6^18 6^3 6^10 6^15 6^21 6^26 6^3 } </pre> =={{header\|Ruby}}== <syntaxhighlight lang="ruby">def smallest_6(n) i = 1 c = 0 s = n.to_s until i.to_s.match?(s) c += 1 i = 6 end [n, c, i] end (0..21).each{\|n\| puts "%3d%-3d: %d" % smallest_6(n) } </syntaxhighlight> {{out}} <pre> 09 : 10077696 10 : 1 23 : 216 32 : 36 46 : 46656 56 : 46656 61 : 6 75 : 7776 812 : 2176782336 94 : 1296 109 : 10077696 1116 : 2821109907456 124 : 1296 1313 : 13060694016 1428 : 6140942214464815497216 1518 : 101559956668416 163 : 216 1710 : 60466176 1815 : 470184984576 1921 : 21936950640377856 2026 : 170581728179578208256 213 : 216 </pre> =={{header\|Wren}}== {{libheader\|Wren-big}} {{libheader\|Wren-fmt}} <~~lang~~syntaxhighlight ~~ecmascript~~lang="wren">import "./big" for BigInt import "./fmt" for Fmt System.print(" n smallest power of 6 which contains n") Line 1,005 ⟶ 1,711: i = i + 1 } }</~~lang~~syntaxhighlight> {{out}} Line 1,033 ⟶ 1,739: 21 6^3 = 216 </pre> =={{header\|Yabasic}}== {{trans\|Python}} <syntaxhighlight lang="yabasic">// Rosetta Code problem: http://rosettacode.org/wiki/Smallest_power_of_6_whose_decimal_expansion_contains_n // by Galileo, 05/2022 sub smallest_six(n) local p, n$ n$ = str$(n) p = 1 while not instr(str$(p, "%1.f"), n$) p = p 6 : wend return p end sub for n = 0 to 21 : print n, ": ", str$(smallest_six(n), "%1.f") : next</syntaxhighlight> {{out}} <pre>0: 10077696 1: 1 2: 216 3: 36 4: 46656 5: 46656 6: 6 7: 7776 8: 2176782336 9: 1296 10: 10077696 11: 2821109907456 12: 1296 13: 13060694016 14: 6140942214464815497216 15: 101559956668416 16: 216 17: 60466176 18: 470184984576 19: 21936950640377856 20: 170581728179578208256 21: 216 ---Program done, press RETURN---</pre>