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A063575
Smallest k such that 4^k has exactly n 0's in its decimal representation.
11
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
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