A084320 Number of powers of two between 2 consecutive factorials (2! including).

1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 6, 5, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 7, 6, 6, 7, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6

Offset: 1

Author

Labos Elemer, Jun 19 2003

Keywords

• nonn

Examples

			n=7: a(7)=3 because between 5040 and 40320 three powers of 2 occur: 8192, 16384 and 32768.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067850, A058033, A000142, A000079.

Programs

Mathematica

Table[Floor[Log[2, (w+1)! ]//N]-Floor[Log[2, w! ]//N], {w, 1, 128}]

PARI

a(n)=if(n<6,(n+1)\2,log((n+1)!)\log(2)-log(n!)\log(2)) \\ Charles R Greathouse IV, Dec 26 2013

Formula

a(n) = A067850(n+1) - A067850(n).

a(n) = A000523(n) + O(1). - Charles R Greathouse IV, Dec 26 2013