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A363743
a(n) = floor(sqrt(log_10(n!))).
0
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
0,9
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.
FORMULA
a(n) = floor(sqrt(A034886(n) - 1)).
a(n) = A000196(A034886(n) - 1).
MATHEMATICA
Array[Floor@ Sqrt[Log10[#!]] &, 93, 0]
PROG
(PARI) a(n) = sqrtint(log(n!)/log(10)); \\ Michel Marcus, Sep 27 2023
CROSSREFS
Sequence in context: A059396 A108602 A305025 * A085290 A108611 A133875
KEYWORD
nonn
AUTHOR
STATUS
approved