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

0,2

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).

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 *)

Prog

(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

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).

Sequence in context: A317693 A145026 A039561 * A302873 A170837 A170876

Adjacent sequences: A063572 A063573 A063574 * A063576 A063577 A063578

Keyword

base,nonn

Author

Robert G. Wilson v, Aug 10 2001

Extensions

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

Status

approved