This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093686 #14 May 16 2025 18:21:25 %S A093686 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, %T A093686 32,33,34,35,36,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,56, %U A093686 57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79 %N A093686 In binary representation: numbers occurring at least once in their factorial. %C A093686 A093684(a(n)) > 0, complement of A093685. %C A093686 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 %H A093686 Harvey P. Dale, <a href="/A093686/b093686.txt">Table of n, a(n) for n = 1..1000</a> %e A093686 6!=1*2*3*4*5*6=720 -> '1011010000' where '110'=6 is contained: %e A093686 '..110.....', therefore 6 is a term. %t A093686 Select[Range[80],SequenceCount[IntegerDigits[#!,2],IntegerDigits[#,2]]>0&] (* _Harvey P. Dale_, May 16 2025 *) %Y A093686 Cf. A036603, A007088, A000142. %K A093686 nonn %O A093686 1,2 %A A093686 _Reinhard Zumkeller_, Apr 10 2004