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

1,2

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A036603, A007088, A000142.

Sequence in context: A070932 A161577 A358330 * A325031 A364433 A155763

Adjacent sequences: A093683 A093684 A093685 * A093687 A093688 A093689

Keyword

nonn

Author

Reinhard Zumkeller, Apr 10 2004

Status

approved