A063575 Smallest k such that 4^k has exactly n 0's in its decimal representation.

0, 5, 21, 35, 47, 44, 50, 51, 103, 99, 121, 125, 126, 175, 166, 131, 185, 153, 184, 223, 272, 232, 248, 336, 233, 306, 315, 384, 314, 327, 333, 373, 393, 399, 454, 457, 504, 453, 484, 506, 621, 494, 510, 639, 522, 557, 560, 559, 716, 609, 629

Offset: 0

Author

Robert G. Wilson v, Aug 10 2001

Keywords

• base
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000 (first 150 terms from Harry J. Smith; a(0) modified by M. F. Hasler).

Crossrefs

Cf. A031146 (analog for 2^k), A063555 (for 3^k), A063585 (for 5^k), A063596 (for 6^k), A063606 (for 7^k), A063616 (for 8^k).

Programs

Mathematica

a = {}; Do[k = 0; While[ Count[ IntegerDigits[4^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
Module[{nn=750,p4},p4=Table[{n,DigitCount[4^n,10,0]},{n,nn}];Transpose[ Table[ SelectFirst[p4,#[[2]]==i&],{i,0,50}]][[1]]] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, May 20 2016 *)

PARI

Count(x, d)= { local(c,f); c=0; while (x>9, f=x-10*(x\10); if (f==d, c++); x\=10); if (x==d, c++); return(c) } { for (n=0, 150, a=0; while (Count(4^a, 0) != n, a++); write("b063575.txt", n, " ", a) ) } \\  Harry J. Smith, Aug 26 2009

PARI

A063575(n)=for(k=n,oo,#select(d->!d,digits(4^k))==n&&return(k)) \\ M. F. Hasler, Jun 14 2018

Extensions

a(0) changed to 0 as in A031146, A063555, ... by M. F. Hasler, Jun 14 2018