A070034 Numbers n such that n! reduced modulo 2^n is also a power of 2.

1, 2, 4, 6, 8, 16, 19, 20, 21, 27, 32, 35, 36, 39, 40, 42, 44, 52, 64, 67, 68, 72, 73, 79, 80, 88, 92, 101, 104, 109, 116, 128, 131, 132, 136, 137, 141, 144, 145, 146, 150, 159, 160, 176, 177, 185, 188, 202, 204, 208, 209, 233, 244, 256, 259, 260, 264, 265

Offset: 1

Author

Labos Elemer, Apr 17 2002

Keywords

• nonn

Examples

			Not rarely,consecutive integers are in the sequence like {19,20,21}, providing residues {65536,262144,262144}.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..800

Crossrefs

Cf. A000142, A000079, A068496.

Programs

Mathematica

t = {}; Do[s=Mod[n!, 2^n]; If[IntegerQ[Log[2, s]], AppendTo[t, n]], {n, 300}]; t
Select[Range[300],IntegerQ[Log2[Mod[#!,2^#]]]&] (* Harvey P. Dale, Aug 04 2021 *)

Formula

Mod[a(n)!, 2^a(n)] = A068496(n) = 2^w for some integer w.