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 A103671 #19 Apr 03 2025 01:42:01
%S A103671 4,5,5,5,6,5,6,5,5,5,5,5,5,5,5,5,6,7,5,6,5,6,5,6,5,5,5,6,6,6,5,7,6,6,
%T A103671 6,6,6,7,6,6,5,6,6,6,6,6,6,5,6,7,6,6,5,6,6,6,6,6,6,5,6,6,6,6,6,7,6,6,
%U A103671 7,6,6,6,6,6,6,7,6,6,6,6,7,6,6,6,6,7,6,6,7,7,6,6,6,7,6,6,7,6,6,6,7,6,7,6,6
%N A103671 Smallest m such that the binary representation of n! does not contain m!.
%C A103671 _Reinhard Zumkeller_ conjectures (at A102730) that this sequence is bounded. I conjecture the contrary, that for every k there is n with a(n) > k. - _Charles R Greathouse IV_, Apr 07 2013
%H A103671 Amiram Eldar, <a href="/A103671/b103671.txt">Table of n, a(n) for n = 6..10000</a>
%H A103671 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A103671 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%t A103671 q[n_, m_] := StringContainsQ[IntegerString[n!, 2], IntegerString[m!, 2]]; a[n_] := Module[{m = 2}, While[q[n, m], m++]; m]; Array[a, 105, 6] (* _Amiram Eldar_, Apr 03 2025 *)
%Y A103671 Cf. A102730, A103672, A036603, A007088, A000142.
%K A103671 nonn,base
%O A103671 6,1
%A A103671 _Reinhard Zumkeller_, Feb 12 2005