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

1,2

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000142, A000079, A068496.

Sequence in context: A160560 A332291 A093109 * A329798 A364814 A353867

Adjacent sequences: A070031 A070032 A070033 * A070035 A070036 A070037

Keyword

nonn

Author

Labos Elemer, Apr 17 2002

Status

approved