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

Author

Robert G. Wilson v, Aug 10 2001

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A000244.

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

Programs

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 *)

PARI

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

Extensions

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