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

1,2

Comments

Sequence is not monotonic.

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.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A370681 A245092 A342126 * A353705 A162906 A378993

Adjacent sequences: A092598 A092599 A092600 * A092602 A092603 A092604

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 08 2004

Status

approved