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A031146 Exponent of the least power of 2 having exactly n zeros in its decimal representation. 16

%I

%S 0,10,42,43,79,88,100,102,189,198,242,250,252,263,305,262,370,306,368,

%T 383,447,464,496,672,466,557,630,629,628,654,657,746,771,798,908,913,

%U 917,906,905,1012,1113,988,1020,989,1044,1114,1120,1118,1221,1218,1255

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

%H T. D. Noe, <a href="/A031146/b031146.txt">Table of n, a(n) for n = 0..1000</a>

%e 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, ...

%t 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 *)

%t 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 *)

%o (PARI) A031146(n)=for(k=0, oo, #select(d->!d, digits(2^k))==n&&return(k)) \\ _M. F. Hasler_, Jun 15 2018

%Y Cf. A000079, A007377, A031147, A006889.

%Y 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).

%K base,nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Erich Friedman_

%E Definition clarified by _Joerg Arndt_, Sep 27 2016

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)