A063616 Smallest k >= 0 such that 8^k has exactly n 0's in its decimal representation.

0, 4, 14, 23, 42, 33, 35, 34, 63, 66, 87, 116, 84, 101, 126, 164, 128, 102, 135, 143, 149, 155, 203, 224, 186, 204, 210, 237, 261, 218, 219, 286, 257, 266, 361, 355, 336, 302, 374, 339, 371, 398, 340, 409, 348, 388, 494, 436, 407, 406, 439

Offset: 0

Author

Robert G. Wilson v, Aug 10 2001

Keywords

• base
• nonn

Crossrefs

Cf. A031146 (analog for 2^k), A063555 (analog for 3^k), A063575 (analog for 4^k), A063585 (for 5^k), A063596 (analog for 6^k), A063606 (analog for 7^k).

Programs

Mathematica

a = {}; Do[k = 0; While[ Count[ IntegerDigits[8^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a

PARI

A063616(n)=for(k=0, oo, #select(d->!d, digits(8^k))==n&&return(k)) \\ M. F. Hasler, Jun 14 2018

Extensions

a(0) changed to 0 (as in A031146, A063555, ...) and better title from M. F. Hasler, Jun 14 2018