A363743 a(n) = floor(sqrt(log_10(n!))).

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, 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, 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

Offset: 0

Author

Paul F. Marrero Romero, Aug 17 2023

Keywords

• nonn

Comments

Every nonnegative integer occurs at least 4 times.

Each integer k > 14 appears fewer than k times.

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

Crossrefs

Cf. A000196, A034886.

Programs

Mathematica

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

PARI

a(n) = sqrtint(log(n!)/log(10)); \\ Michel Marcus, Sep 27 2023

Formula

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

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