A092601 Number of numbers from 1 to n whose binary representation is contained in that of n!.

1, 2, 3, 4, 4, 6, 7, 8, 8, 9, 9, 9, 12, 14, 14, 15, 16, 17, 18, 19, 20, 21, 23, 23, 24, 26, 26, 28, 28, 30, 27, 28, 33, 34, 35, 35, 34, 37, 39, 38, 40, 42, 43, 43, 44, 45, 43, 46, 48, 48, 51, 51, 53, 53, 53, 55, 56, 58, 55, 59, 61, 62, 63, 64, 64, 66, 65, 68, 68, 70, 70, 71, 73

Offset: 1

Author

Reinhard Zumkeller, Apr 08 2004

Keywords

• nonn
• base

Comments

Sequence is not monotonic.

Examples

			n = 5: 5! = 1*2*3*4*5 = 120 = '1111000': 1 = '1', 2 = '10', 3 = '11' and 4 = '100' are contained, but not 5 = '101', therefore a(5) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A000142, A007088, A036603, A093710, A093711.

Programs

Mathematica

f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; g[n_] := Block[{c = 0, k = 1, s = f[n! ]}, While[k <= n, If[ StringPosition[ s, f[k]] != {}, c++ ]; k++ ]; c]; Table[ g[n], {n, 75}] (* Robert G. Wilson v, Apr 21 2004 *)

Formula

a(A093710(n)) = n, a(A093711(n)) < n.