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 A103681 #20 Apr 03 2025 01:33:58 %S A103681 0,1,2,3,4,5,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26, %T A103681 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49, %U A103681 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73 %N A103681 Numbers m such that in binary representation m! does not contain 7!. %C A103681 Last term is probably 5153, since all numbers from 5154 to 5*10^5 do not belong to the sequence. - _Giovanni Resta_, Apr 07 2013 %H A103681 Amiram Eldar, <a href="/A103681/b103681.txt">Table of n, a(n) for n = 1..1041</a> %H A103681 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>. %H A103681 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>. %F A103681 A103675(a(n)) = 0, A103675(A103680(n)) = 1. %t A103681 Select[Range[0, 100], !StringContainsQ[IntegerString[#!, 2], IntegerString[7!, 2]] &] (* _Amiram Eldar_, Apr 03 2025 *) %o A103681 (PARI) is(n)=n=n!; while(n>5039, my(e=valuation(n, 2), e1=valuation((n>>=e)+1, 2)); n>>=e1; if(e>3 && e1==2 && bitand(n, 127)==78, return(0))); 1 \\ _Charles R Greathouse IV_, Apr 07 2013 %Y A103681 Complement of A103680. %Y A103681 Cf. A000142, A007088, A036603, A102730, A103677, A103679. %K A103681 base,nonn %O A103681 1,3 %A A103681 _Reinhard Zumkeller_, Feb 12 2005