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 A363743 #42 Nov 22 2023 22:10:59 %S A363743 0,0,0,0,1,1,1,1,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6, %T A363743 6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9, %U A363743 9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11 %N A363743 a(n) = floor(sqrt(log_10(n!))). %C A363743 Every nonnegative integer occurs at least 4 times. %C A363743 Each integer k > 14 appears fewer than k times. %C A363743 The only integers k that occur exactly k times are 11, 13 and 14. %F A363743 a(n) = floor(sqrt(A034886(n) - 1)). %F A363743 a(n) = A000196(A034886(n) - 1). %t A363743 Array[Floor@ Sqrt[Log10[#!]] &, 93, 0] %o A363743 (PARI) a(n) = sqrtint(log(n!)/log(10)); \\ _Michel Marcus_, Sep 27 2023 %Y A363743 Cf. A000196, A034886. %K A363743 nonn %O A363743 0,9 %A A363743 _Paul F. Marrero Romero_, Aug 17 2023