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 A072831 #20 Oct 27 2021 21:53:15 %S A072831 1,1,2,3,5,7,10,13,16,19,22,26,29,33,37,41,45,49,53,57,62,66,70,75,80, %T A072831 84,89,94,98,103,108,113,118,123,128,133,139,144,149,154,160,165,170, %U A072831 176,181,187,192,198,203,209,215,220,226,232,238,243,249,255,261,267 %N A072831 Number of bits in n!. %H A072831 Alois P. Heinz, <a href="/A072831/b072831.txt">Table of n, a(n) for n = 0..10000</a> %H A072831 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a> %F A072831 a(n) = floor(log(n!)/log(2)) + 1. %e A072831 a(4)=5 because 4! = 4*3*2*1 = 24 (base 10) = 11000 (base 2), using 5 bits. %p A072831 a:= n-> 1+ilog2(n!): %p A072831 seq(a(n), n=0..100); # _Alois P. Heinz_, May 03 2016 %t A072831 Floor[Log[2,Range[0,60]!]]+1 (* _Harvey P. Dale_, Nov 16 2011 *) %o A072831 (PARI) for(n=0,100,print1(floor(log(n!)/log(2))+1,",")) %o A072831 (PARI) a(n) = #binary(n!); \\ _Michel Marcus_, Dec 23 2016 %o A072831 (Python) %o A072831 import math %o A072831 def a(n): %o A072831 return len(bin(math.factorial(n))[2:]) # _Indranil Ghosh_, Dec 23 2016 %Y A072831 Cf. A034886 (decimal digits of n!), A000142 (n!). Essentially the same as A003070. %K A072831 base,nonn %O A072831 0,3 %A A072831 _Rick L. Shepherd_, Jul 22 2002