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

Author

Reinhard Zumkeller, Apr 11 2004

Keywords

• nonn
• base

Examples

			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
		

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

Crossrefs

Complement of A093711.

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

Formula

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