A063555 Smallest k such that 3^k has exactly n 0's in its decimal representation.

0, 10, 22, 21, 35, 57, 55, 54, 107, 137, 126, 170, 188, 159, 191, 225, 259, 297, 262, 253, 340, 296, 380, 369, 403, 395, 383, 407, 429, 514, 446, 486, 431, 545, 589, 510, 546, 542, 666, 733, 540, 621, 709, 715, 549, 694, 804, 820, 847, 865, 710

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..2000

Maple

N:= 100: # to get a(0)..a(N)
A:= Array(0..N, -1):
p:= 1: A[0]:= 0:
count:= 1:
for k from 1 while count <= N do
  p:= 3*p;
  m:= numboccur(0, convert(p, base, 10));
  if m <= N and A[m] < 0 then A[m]:= k; count:= count+1 fi
od:
seq(A[i], i=0..N); # Robert Israel, Dec 21 2016

Mathematica

a = {}; Do[k = 1; While[ Count[ IntegerDigits[3^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
Module[{l3=Table[{n, DigitCount[3^n, 10, 0]}, {n, 900}]}, Transpose[Table[ SelectFirst[ l3, #[[2]]==i&], {i, 0, 50}]][[1]]] (* Harvey P. Dale, Dec 08 2014 *)

Prog

(PARI) A063555(n)=for(k=0, oo, #select(d->!d, digits(3^k))==n&&return(k)) \\ M. F. Hasler, Jun 14 2018

Crossrefs

Cf. A000244.

Cf. A031146 (analog for 2^k), A063575 (analog for 4^k).

Sequence in context: A226789 A110367 A104865 * A228010 A303745 A303746

Adjacent sequences: A063552 A063553 A063554 * A063556 A063557 A063558

Keyword

base,nonn

Author

Robert G. Wilson v, Aug 10 2001

Extensions

a(0) corrected by Zak Seidov, Jun 14 2018

Status

approved