A093686 In binary representation: numbers occurring at least once in their factorial.

1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset: 1

Author

Reinhard Zumkeller, Apr 10 2004

Keywords

• nonn

Comments

A093684(a(n)) > 0, complement of A093685.

Almost all numbers are included -- of the first 1000 numbers, only 14 -- i.e., 5, 11, 13, 15, 17, 31, 37, 55, 81, 164, 395, 513, 517, and 619 -- do not appear. In all likelihood, the density of such exceptions gets even smaller as the numbers get larger. - Harvey P. Dale, May 16 2025

Examples

			6!=1*2*3*4*5*6=720 -> '1011010000' where '110'=6 is contained:
'..110.....', therefore 6 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A036603, A007088, A000142.

Programs

Mathematica

Select[Range[80],SequenceCount[IntegerDigits[#!,2],IntegerDigits[#,2]]>0&] (* Harvey P. Dale, May 16 2025 *)