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

0,4

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.

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A000142, A007088, A036603, A038374.

Sequence in context: A363219 A371531 A238745 * A221861 A057939 A163371

Adjacent sequences: A092604 A092605 A092606 * A092608 A092609 A092610

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2004

Status

approved