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 A092601 #20 Aug 05 2025 03:38:38
%S A092601 1,2,3,4,4,6,7,8,8,9,9,9,12,14,14,15,16,17,18,19,20,21,23,23,24,26,26,
%T A092601 28,28,30,27,28,33,34,35,35,34,37,39,38,40,42,43,43,44,45,43,46,48,48,
%U A092601 51,51,53,53,53,55,56,58,55,59,61,62,63,64,64,66,65,68,68,70,70,71,73
%N A092601 Number of numbers from 1 to n whose binary representation is contained in that of n!.
%C A092601 Sequence is not monotonic.
%H A092601 Amiram Eldar, <a href="/A092601/b092601.txt">Table of n, a(n) for n = 1..10000</a>
%H A092601 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A092601 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A092601 a(A093710(n)) = n, a(A093711(n)) < n.
%e A092601 n = 5: 5! = 1*2*3*4*5 = 120 = '1111000': 1 = '1', 2 = '10', 3 = '11' and 4 = '100' are contained, but not 5 = '101', therefore a(5) = 4.
%t A092601 f[n_] := ToString[ FromDigits[ IntegerDigits[n, 2]]]; g[n_] := Block[{c = 0, k = 1, s = f[n! ]}, While[k <= n, If[ StringPosition[ s, f[k]] != {}, c++ ]; k++ ]; c]; Table[ g[n], {n, 75}] (* _Robert G. Wilson v_, Apr 21 2004 *)
%Y A092601 Cf. A000142, A007088, A036603, A093710, A093711.
%K A092601 nonn,base
%O A092601 1,2
%A A092601 _Reinhard Zumkeller_, Apr 08 2004