A093710 Numbers k such that in their binary representation all numbers from 1 to k are contained in k!.

1, 2, 3, 4, 6, 7, 8, 14, 23, 26, 28, 30, 33, 34, 35, 39, 42, 43, 51, 53, 58, 61, 62, 63, 64, 66, 68, 70, 73, 77, 80, 83, 93, 94, 106, 108, 111, 114, 115, 116, 126, 131, 132, 133, 134, 136, 137, 147, 149, 153, 155, 156, 169, 172, 175, 180, 185, 187, 191, 195, 206

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 3773 terms from Amiram Eldar)

David A. Corneth, Plot of a(n+1)-a(n), n = 1..9999

David A. Corneth, plot of a(n)/n, n = 1..10000

Formula

A092601(a(n)) = a(n).

Example

6 is in the sequence because 6! = 1011010000_2 which contains 4 = 100_2, 5 = 101_2 and 6 = 110_2 as a substring in the binary expansion. As it contains 4, 5 and 6 in binary it contains the binary expansion of every smaller number than 4 in its binary expansion. - David A. Corneth, Aug 05 2025

Crossrefs

Complement of A093711.

Cf. A000142, A007088, A036603, A072831, A092601.

Sequence in context: A257648 A096360 A039087 * A091421 A138936 A135604

Adjacent sequences: A093707 A093708 A093709 * A093711 A093712 A093713

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 11 2004

Status

approved