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 A103672 #17 Apr 03 2025 02:53:41
%S A103672 0,1,2,3,4,3,4,7,4,5,4,5,4,4,4,15,4,4,4,6,4,5,6,4,5,4,5,4,5,6,6,31,5,
%T A103672 5,5,4,6,5,5,5,5,5,6,5,5,4,5,5,5,5,5,5,6,5,6,5,5,6,5,5,5,5,5,63,6,5,5,
%U A103672 5,5,5,6,5,5,6,5,5,5,5,5,5,6,5,5,5,5,6,5,5,5,5,6,5,5,6,6,5,5,5,6,7,5,6,5,5
%N A103672 Greatest m < n such that the binary representation of n! contains m!.
%H A103672 Amiram Eldar, <a href="/A103672/b103672.txt">Table of n, a(n) for n = 1..10000</a>
%H A103672 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A103672 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A103672 a(2^k) = 2^k - 1, a(A000079(k)) = A000225(k).
%t A103672 q[n_, m_] := StringContainsQ[IntegerString[n!, 2], IntegerString[m!, 2]]; a[n_] := Module[{m = n-1}, While[!q[n, m], m--]; m]; Array[a, 104] (* _Amiram Eldar_, Apr 03 2025 *)
%Y A103672 Cf. A000079, A000225, A102730, A103671, A036603, A007088, A000142.
%K A103672 nonn,base
%O A103672 1,3
%A A103672 _Reinhard Zumkeller_, Feb 12 2005