A092607 Length of longest contiguous block of ones in binary representation of n!.

1, 1, 1, 2, 2, 4, 2, 3, 3, 2, 5, 2, 6, 3, 3, 3, 3, 6, 5, 3, 5, 5, 5, 6, 4, 6, 6, 6, 4, 5, 6, 3, 3, 7, 6, 5, 5, 12, 8, 10, 8, 5, 5, 7, 6, 5, 8, 9, 8, 6, 4, 6, 7, 7, 7, 6, 8, 5, 8, 8, 7, 5, 9, 8, 8, 7, 7, 11, 7, 7, 8, 14, 10, 9, 7, 7, 7, 6, 7, 8, 10, 8, 10, 9, 7, 7, 5, 7, 7, 7, 9, 8, 7, 8, 10, 6, 8, 7

Offset: 0

Author

Reinhard Zumkeller, Apr 11 2004

Keywords

• nonn
• base

Examples

			n = 10: 10! = 3628800 = '1101110101111100000000' = '.........11111........': a(10) = 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A000142, A007088, A036603, A038374.

Programs

Mathematica

a[n_] := Max[Length /@ Split[IntegerDigits[n!, 2]][[1 ;; -1 ;; 2]]]; Array[a, 100, 0] (* Amiram Eldar, Jul 29 2025 *)

Formula

a(n) = A038374(A000142(n)).