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 A058885 a(n) = smallest k such that k! ends in 2^n, not counting the trailing zeros. 1
 0, 2, 4, 9, 12, 8, 20, 33, 159, 43, 49, 348, 60, 91, 8134, 1964, 1392, 735, 34060, 9030, 14052, 39306, 16906, 29338, 53711, 356449, 88137, 543041, 1435398, 1000154, 5037980, 2245246, 499245, 6240345, 2989574, 34190394, 11257817, 146038526 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE a(4) = 12 because 12! = 479001600. When you delete the trailing zeros, you have 4790016 which ends in 16 = 2^4. MATHEMATICA f[n_] := Block[{a = 2^n, k = 1, len = 10^Floor[ Log[10, 2^n] + 1], p = 1}, While[ Mod[p, len] != a, p = k*p; While[ Mod[p, 10] == 0, p /= 10]; p = Mod[p, 100*len]; k++ ]; k - 1]; lst = {}; Do[ AppendTo[ lst, f@n], {n, 0, 37}] CROSSREFS Cf. A059449. Sequence in context: A292769 A307997 A096134 * A256446 A022428 A096186 Adjacent sequences:  A058882 A058883 A058884 * A058886 A058887 A058888 KEYWORD nonn AUTHOR Robert G. Wilson v, Jan 07 2001 EXTENSIONS a(15) corrected, a(18) through a(37) and better definition from Jon E. Schoenfield Sep 02 2009. STATUS approved

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Last modified August 7 08:08 EDT 2020. Contains 336274 sequences. (Running on oeis4.)