login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = floor(sqrt(log_10(n!))).
0

%I #42 Nov 22 2023 22:10:59

%S 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 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 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 a(n) = floor(sqrt(log_10(n!))).

%C Every nonnegative integer occurs at least 4 times.

%C Each integer k > 14 appears fewer than k times.

%C The only integers k that occur exactly k times are 11, 13 and 14.

%F a(n) = floor(sqrt(A034886(n) - 1)).

%F a(n) = A000196(A034886(n) - 1).

%t Array[Floor@ Sqrt[Log10[#!]] &, 93, 0]

%o (PARI) a(n) = sqrtint(log(n!)/log(10)); \\ _Michel Marcus_, Sep 27 2023

%Y Cf. A000196, A034886.

%K nonn

%O 0,9

%A _Paul F. Marrero Romero_, Aug 17 2023