A031146 Exponent of the least power of 2 having exactly n zeros in its decimal representation.

0, 10, 42, 43, 79, 88, 100, 102, 189, 198, 242, 250, 252, 263, 305, 262, 370, 306, 368, 383, 447, 464, 496, 672, 466, 557, 630, 629, 628, 654, 657, 746, 771, 798, 908, 913, 917, 906, 905, 1012, 1113, 988, 1020, 989, 1044, 1114, 1120, 1118, 1221, 1218, 1255

Offset: 0

Author

N. J. A. Sloane

Keywords

• base
• nonn

Examples

			a(3) = 43 since 2^m contains 3 0's for m starting with 43 (2^43 = 8796093022208) and followed by 53, 61, 69, 70, 83, 87, 89, 90, 93, ...
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000079, A007377, A031147, A006889.

Cf. A063555 (analog for 3^k), A063575 (for 4^k), A063585 (for 5^k), A063596 (for 6^k), A063606 (for 7^k), A063616 (for 8^k), A063626 (for 9^k).

Programs

Mathematica

a = {}; Do[k = 0; While[ Count[ IntegerDigits[2^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a (* Robert G. Wilson v, Jun 12 2004 *)
nn = 100; t = Table[0, {nn}]; found = 0; k = 0; While[found < nn, k++; cnt = Count[IntegerDigits[2^k], 0]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = k; found++]]; t = Join[{0}, t] (* T. D. Noe, Mar 14 2012 *)

PARI

A031146(n)=for(k=0, oo, #select(d->!d, digits(2^k))==n&&return(k)) \\ M. F. Hasler, Jun 15 2018

Extensions

More terms from Erich Friedman

Definition clarified by Joerg Arndt, Sep 27 2016