Smallest power of 6 whose decimal expansion contains n
- Task
Show the smallest (non-negative integer) power of 6 whose decimal expansion contains n, where n < 22
C
<lang C>#include <stdio.h>
- include <string.h>
- include <gmp.h>
char *power_of_six(unsigned int n, char *buf) {
mpz_t p; mpz_init(p); mpz_ui_pow_ui(p, 6, n); mpz_get_str(buf, 10, p); mpz_clear(p); return buf;
}
char *smallest_six(unsigned int n) {
static char nbuf[32], powbuf[1024];
unsigned int p = 0;
do {
sprintf(nbuf, "%u", n);
power_of_six(p++, powbuf);
} while (!strstr(powbuf, nbuf));
return powbuf;
}
int main() {
unsigned int i;
for (i=0; i<22; i++) {
printf("%d: %s\n", i, smallest_six(i));
}
return 0;
}</lang>
- Output:
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
F#
<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 (e*6I) (e*6I) |(_,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)) </lang>
- Output:
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 23 2176782336 24 1023490369077469249536 25 170581728179578208256 26 16926659444736 27 279936 28 2821109907456 29 1296 30 13060694016 31 131621703842267136 32 4738381338321616896 33 2176782336 34 1023490369077469249536 35 609359740010496 36 36 37 21936950640377856 38 131621703842267136 39 221073919720733357899776 40 13060694016 41 78364164096 42 131621703842267136 43 28430288029929701376 44 16926659444736 45 470184984576 46 46656 47 470184984576 48 6140942214464815497216 49 470184984576 50 21936950640377856 51 1326443518324400147398656 52 623673825204293256669089197883129856 53 789730223053602816 54 6140942214464815497216 55 101559956668416 56 46656 57 470184984576 58 3656158440062976 59 16926659444736 60 60466176 61 1679616 62 362797056 63 47751966659678405306351616 64 78364164096 65 46656 66 46656 67 1679616 68 101559956668416 69 10077696 70 362797056 71 131621703842267136 72 170581728179578208256 73 16926659444736 74 2821109907456 75 47751966659678405306351616 76 7776 77 7776 78 2176782336 79 279936 80 28430288029929701376 81 789730223053602816 82 2176782336 83 78364164096 84 470184984576 85 21936950640377856 86 36845653286788892983296 87 61886548790943213277031694336 88 28430288029929701376 89 789730223053602816 90 2821109907456 91 221073919720733357899776 92 16926659444736 93 279936 94 13060694016 95 101559956668416 96 1296 97 362797056 98 470184984576 99 279936 Real: 00:00:00.066
Factor
<lang factor>USING: formatting kernel lists lists.lazy math math.functions present sequences tools.memory.private ;
- powers-of-6 ( -- list )
0 lfrom [ 6 swap ^ ] lmap-lazy ;
- smallest ( m -- n )
present powers-of-6 [ present subseq? ] with lfilter car ;
22 [ dup smallest commas "%2d %s\n" printf ] each-integer</lang>
- Output:
0 10,077,696 1 1 2 216 3 36 4 46,656 5 46,656 6 6 7 7,776 8 2,176,782,336 9 1,296 10 10,077,696 11 2,821,109,907,456 12 1,296 13 13,060,694,016 14 6,140,942,214,464,815,497,216 15 101,559,956,668,416 16 216 17 60,466,176 18 470,184,984,576 19 21,936,950,640,377,856 20 170,581,728,179,578,208,256 21 216
Haskell
<lang haskell>import Control.Monad import Data.List import Text.Printf
sixes :: [Integer] sixes = iterate (*6) 1
smallest :: Integer -> Integer smallest n = head $ filter (\r -> show n `isInfixOf` show r) sixes
main :: IO () main = putStr $ concatMap (printf "%2d: %d\n" `ap` smallest) [0..21]</lang>
- Output:
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
Julia
<lang julia>using Formatting
digcontains(n, dig) = contains(String(Char.(digits(n))), String(Char.(dig)))
function findpow6containing(needle)
dig = digits(needle)
for i in 0:1000
p = big"6"^i
digcontains(p, dig) && return p
end
error("could not find a power of 6 containing $dig")
end
for n in 0:21
println(rpad(n, 5), format(findpow6containing(n), commas=true))
end
</lang>
- Output:
0 10,077,696 1 1 2 216 3 36 4 46,656 5 46,656 6 6 7 7,776 8 2,176,782,336 9 1,296 10 10,077,696 11 2,821,109,907,456 12 1,296 13 13,060,694,016 14 6,140,942,214,464,815,497,216 15 101,559,956,668,416 16 216 17 60,466,176 18 470,184,984,576 19 21,936,950,640,377,856 20 170,581,728,179,578,208,256 21 216
Pascal
Doing long multiplikation like in primorial task. <lang pascal>program PotOf6; {$IFDEF FPC} {$MODE DELPHI} {$ENDIF} uses
sysutils,strutils;
const // POT_LIMIT = 6260;DEC_LIMIT = 1000000;//'575115' in 6^6260 // POT_LIMIT = 1736;DEC_LIMIT = 100000;
//'83081' in 6^1736 mean power 422.48
// POT_LIMIT = 444; DEC_LIMIT = 10000;
//'2565' mean power 135.82 0.157s
// POT_LIMIT = 147; DEC_LIMIT = 1000;
//'120' mean power 44.21
// POT_LIMIT = 46; DEC_LIMIT = 100;
//'52' mean power 15.71 POT_LIMIT = 28;DEC_LIMIT = 22; //'14' mean power 9.73
type
tMulElem = Uint32; tMul = array of tMulElem;
var
Pot_N_str : array of AnsiString; T0,maxPow,PowerSum,lastpot,SumLenght : INt64;
procedure ConvToStr(var s:Ansistring;const Mul:tMul); var
s9: string[9]; pS : pChar; i,j,k : NativeInt;
begin
i := High(MUL);
j := (i+1)*9;
setlength(s,j+1);
pS := pChar(s);
// fill complete with '0'
fillchar(pS[0],j,'0');
str(Mul[i],S9);
j := length(s9);
move(s9[1],pS[0],j);
k := j;
dec(i);
If i >= 0 then
repeat
str(Mul[i],S9);// no leading '0'
j := length(s9);
inc(k,9);
//move to the right place, leading '0' is already there
move(s9[1],pS[k-j],j);
dec(i);
until i<0;
setlength(s,k);
inc(SumLenght,k);
end;
function Mul_N(var Mul:tMul;n:Uint64):tMul; //n<LongWordDec ! const
LongWordDec = 1000*1000*1000;
var
prod,carry : Uint64; j : NativeInt;
begin
Setlength(result,length(Mul)+1); carry := 0; For j := 0 to High(Mul) do Begin prod := n*Mul[j]+Carry; Carry := prod Div LongWordDec; result[j] := Prod - Carry*LongWordDec; end; IF Carry <> 0 then result[High(Mul)+1] := Carry else Setlength(result,length(Mul));
end;
procedure OutS(const s:Ansistring;j:nativeInt); begin
writeln(s,' ',j);
end;
procedure GeneratePot_N_Str(number:NativeInt); var
PotArrN : array[0..1] of tMul; i,toggle : NativeInt;
Begin
setlength(Pot_N_str,POT_LIMIT+1); Pot_N_str[0] := '1'; Pot_N_str[1] := IntToStr(number);
setlength(PotArrN[0],1); setlength(PotArrN[1],1); PotArrN[0,0] := 1; PotArrN[1,0] := number;
//create all pot of numbers up to number**POT_LIMIT with clean up in parallel
SumLenght :=0;
i := 2;
toggle := 0;
while i <= POT_LIMIT do
begin
PotArrN[toggle] := Mul_N(PotArrN[1-toggle],number);
ConvToStr(Pot_N_str[i],PotArrN[toggle]);
toggle := 1-toggle;
inc(i);
end;
writeln(' used by strings ',Numb2USA(IntToStr(SumLenght)),' bytes');
end; procedure OutT(const s: Ansistring;j:NativeInt); Begin
writeln(j:10,maxPow/(j+1):8:2,(maxPow-lastPot)/1024:8:2,(GetTickCount64-T0)/1000:10:3); T0 := GetTickCount64; lastpot := maxPow;
end; var
s: ansistring; i,j,number: Int32;
Begin
number := 6;
T0 := GetTickCount64;
GeneratePot_N_Str(number);
writeln('Generating time to power limit ',(GetTickCount64-T0)/1000:5:3,'s');
T0 := GetTickCount64;
maxPow := 0;
lastpot := 0;
For i := 0 to DEC_LIMIT-1 do
begin
str(i,s);
For j := 0 to POT_LIMIT do
Begin
if Pos(s,Pot_N_str[j])>0 then
Begin
IF maxPow<j then
maxPow := J;
PowerSum +=j;
IF POT_Limit > 99 then
write(s:3,number:3,'^',j:5,maxPow:6,#13)
else
writeln(s:3,number:3,'^',j:2,' ', Pot_N_str[j]);
break;
end;
end;
end;
writeln;
writeln('mean power to find string',PowerSum/DEC_LIMIT:8:2);
end.</lang>
- Output:
used by strings 330 Generating time to power limit 0.000s 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 mean power to find string 9.73 //Search strings 0 to 99999 used by strings 1,174,099 bytes Generating time to power limit 0.008s 99999 6^ 1287 1736 mean power to find string 422.48 real 0m14,684s user 0m14,522s
Perl
<lang perl>use strict; use warnings; use List::Util 'first'; use Math::AnyNum ':overload';
sub comma { reverse ((reverse shift) =~ s/(.{3})/$1,/gr) =~ s/^,//r }
for my $n (0..21, 314159) {
my $e = first { 6**$_ =~ /$n/ } 0..1000;
printf "%7d: 6^%-3s %s\n", $n, $e, comma 6**$e;
}</lang>
- Output:
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
314159: 6^494 2,551,042,473,957,557,281,758,472,595,966,885,638,262,058,644,568,332,160,010,313,393,465,384,231,415,969,801,503,269,402,221,368,959,426,761,447,049,526,922,498,341,120,174,041,236,629,812,681,424,262,988,020,546,286,492,213,224,906,594,147,652,459,693,833,191,626,748,973,370,777,591,205,509,673,825,541,899,874,436,305,798,094,943,728,762,682,333,192,202,041,960,669,401,031,964,634,164,426,985,990,195,192,836,400,994,016,666,910,919,499,884,972,133,471,176,804,190,463,444,807,178,864,658,551,422,631,018,496
Phix
Another good opportunity to do some string math, this time with embedded commas. Scales effortlessly.
(Related recent task: Show_the_(decimal)_value_of_a_number_of_1s_appended_with_a_3,_then_squared#Phix)
constant lim = 22 -- (tested to 10,000,000) atom t0 = time(), t1 = t0+1 sequence res = repeat(0,lim), pwr = repeat(0,lim) string p6 = "1" res[2] = p6 integer found = 1, p = 0 while found<lim do integer carry = 0 for i=length(p6) to 1 by -1 do if p6[i]!=',' then integer digit = (p6[i]-'0')*6+carry p6[i] = remainder(digit,10)+'0' carry = floor(digit/10) end if end for if carry then if remainder(length(p6)+1,4)=0 then p6 = "," & p6 end if p6 = carry+'0' & p6 end if p += 1 for i=1 to length(p6) do if p6[i]!=',' then integer digit = 0, j = i while j<=length(p6) and digit<=lim do j += p6[j]=',' digit = digit*10+p6[j]-'0' if digit<lim and res[digit+1]=0 then res[digit+1] = p6 pwr[digit+1] = p found += 1 end if j += 1 end while end if end for if time()>t1 then progress("found %,d/%,d, at 6^%,d which has %,d digits (%s)", {found,lim,p,length(p6)*3/4,elapsed(time()-t0)}) t1 = time()+1 end if end while papply(true,printf,{1,{"%2d %29s = 6^%d\n"},shorten(columnize({tagset(lim-1,0),res,pwr}),"",10)})
- Output:
0 10,077,696 = 6^9 1 1 = 6^0 2 216 = 6^3 3 36 = 6^2 4 46,656 = 6^6 5 46,656 = 6^6 6 6 = 6^1 7 7,776 = 6^5 8 2,176,782,336 = 6^12 9 1,296 = 6^4 10 10,077,696 = 6^9 11 2,821,109,907,456 = 6^16 12 1,296 = 6^4 13 13,060,694,016 = 6^13 14 6,140,942,214,464,815,497,216 = 6^28 15 101,559,956,668,416 = 6^18 16 216 = 6^3 17 60,466,176 = 6^10 18 470,184,984,576 = 6^15 19 21,936,950,640,377,856 = 6^21 20 170,581,728,179,578,208,256 = 6^26 21 216 = 6^3
A limit of 10,000,000 takes 1 min 41s, reaches 6^21,798 which has 16,963 digits (not including commas) and is the first to contain 8091358, at offset 13,569.
Raku
<lang perl6>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;
put join "\n", (flat ^22, 120).map: -> $n {
sprintf "%3d: 6%-4s %s", $n, .&super, comma @po6[$_] given @po6.first: *.contains($n), :k
};</lang>
- Output:
0: 6⁹ 10,077,696 1: 6⁰ 1 2: 6³ 216 3: 6² 36 4: 6⁶ 46,656 5: 6⁶ 46,656 6: 6¹ 6 7: 6⁵ 7,776 8: 6¹² 2,176,782,336 9: 6⁴ 1,296 10: 6⁹ 10,077,696 11: 6¹⁶ 2,821,109,907,456 12: 6⁴ 1,296 13: 6¹³ 13,060,694,016 14: 6²⁸ 6,140,942,214,464,815,497,216 15: 6¹⁸ 101,559,956,668,416 16: 6³ 216 17: 6¹⁰ 60,466,176 18: 6¹⁵ 470,184,984,576 19: 6²¹ 21,936,950,640,377,856 20: 6²⁶ 170,581,728,179,578,208,256 21: 6³ 216 120: 6¹⁴⁷ 2,444,746,349,972,956,194,083,608,044,935,243,159,422,957,210,683,702,349,648,543,934,214,737,968,217,920,868,940,091,707,112,078,529,114,392,164,827,136
REXX
<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 6**N */ parse arg hi . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 22 /*Not specified? Then use the default.*/ w= 50 /*width of a number in any column. */
@smp6= ' smallest power of six (expressed in decimal) which contains N'
say ' N │ power │'center(@smp6, 20 + w ) /*display the title of the output. */ say '─────┼───────┼'center("" , 20 + w, '─') /* " " separator " " " */
do j=0 for hi /*look for a power of 6 that contains N*/
do p=0; x= 6**p /*compute a power of six (in decimal). */
if pos(j, x)>0 then leave /*does the power contain an N ? */
end /*p*/
c= commas(x) /*maybe add commas to the powe of six. */
z= right(c, max(w, length(c) ) ) /*show a power of six, allow biger #s. */
say center(j, 5)'│'center(p, 7)"│" z /*display what we have so far (cols). */
end /*j*/
say '─────┴───────┴'center("" , 20 + w, '─') /* " " separator " " " */ 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>
- output when using the default input:
N │ power │ smallest power of six (expressed in decimal) which contains N ─────┼───────┼────────────────────────────────────────────────────────────────────── 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 ─────┴───────┴──────────────────────────────────────────────────────────────────────
Ring
<lang ring> load "stdlib.ring"
decimals(0) see "working..." + nl see "Smallest power of 6 whose decimal expansion contains n:" + nl
num = 0 limit = 200
for n = 1 to 21
strn = string(n)
for m = 0 to limit
strpow = string(pow(6,m))
ind = substr(strpow,strn)
if ind > 0
see "" + n + ". " + "6^" + m + " = " + strpow + nl
exit
ok
next
next
see "done..." + nl </lang>
- Output:
working... Smallest power of 6 whose decimal expansion contains n: 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 done...
Wren
<lang ecmascript>import "/big" for BigInt import "/fmt" for Fmt
System.print(" n smallest power of 6 which contains n") var six = BigInt.new(6) for (n in 0..21) {
var i = 0
while (true) {
var pow6 = six.pow(i).toString
if (pow6.contains(n.toString)) {
Fmt.print("$2d 6^$-2d = $,s", n, i, pow6)
break
}
i = i + 1
}
}</lang>
- Output:
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