A063606 Smallest k >= 0 such that 7^k has exactly n 0's in its decimal representation.

0, 4, 9, 13, 25, 55, 39, 41, 45, 70, 69, 65, 75, 107, 109, 134, 167, 142, 156, 196, 157, 205, 214, 180, 213, 183, 162, 251, 263, 276, 268, 290, 306, 295, 369, 313, 332, 293, 353, 340, 357, 387, 367, 476, 334, 509, 363, 474, 454, 488, 453

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).

Programs

Mathematica

a = {}; Do[k = 0; While[ Count[ IntegerDigits[7^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
Module[{p7=DigitCount[#,10,0]&/@(7^Range[600]),nn=60},Join[{0},Flatten[ Table[ Position[p7,n,1,1],{n,nn}]]]] (* Harvey P. Dale, Apr 12 2022 *)

PARI

A063606(n)=for(k=n, oo, #select(d->!d, digits(5^k))==n&&return(k)) \\ M. F. Hasler, Jun 14 2018