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 A084320 #8 Dec 26 2013 11:00:57
%S A084320 1,1,2,2,3,3,3,3,3,4,3,4,4,4,4,4,4,4,5,4,4,5,5,4,5,5,4,5,5,5,5,5,5,5,
%T A084320 6,5,5,5,6,5,5,6,5,6,5,6,5,6,6,5,6,6,6,5,6,6,6,6,6,6,6,5,6,7,6,6,6,6,
%U A084320 6,6,6,6,7,6,6,6,7,6,6,7,6,6,7,6,7,6,7,6,6,7,7,6,7,6,7,6,7,7,6,7,7,6,7,7,6
%N A084320 Number of powers of two between 2 consecutive factorials (2! including).
%H A084320 Charles R Greathouse IV, <a href="/A084320/b084320.txt">Table of n, a(n) for n = 1..10000</a>
%F A084320 a(n) = A067850(n+1) - A067850(n).
%F A084320 a(n) = A000523(n) + O(1). - _Charles R Greathouse IV_, Dec 26 2013
%e A084320 n=7: a(7)=3 because between 5040 and 40320 three powers of 2 occur: 8192, 16384 and 32768.
%t A084320 Table[Floor[Log[2, (w+1)! ]//N]-Floor[Log[2, w! ]//N], {w, 1, 128}]
%o A084320 (PARI) a(n)=if(n<6,(n+1)\2,log((n+1)!)\log(2)-log(n!)\log(2)) \\ _Charles R Greathouse IV_, Dec 26 2013
%Y A084320 Cf. A067850, A058033, A000142, A000079.
%K A084320 nonn
%O A084320 1,3
%A A084320 _Labos Elemer_, Jun 19 2003