A058885 a(n) = smallest k such that k! ends in 2^n, not counting the trailing zeros.

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

Offset

0,2

Links

Table of n, a(n) for n=0..37.

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