A079692 Number of 7's in n!.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 1, 3, 0, 1, 2, 6, 2, 1, 0, 0, 1, 1, 3, 0, 4, 1, 1, 2, 2, 4, 3, 4, 4, 4, 3, 3, 4, 4, 4, 1, 2, 8, 5, 5, 3, 8, 5, 7, 4, 9, 4, 4, 7, 7, 6, 8, 8, 3, 9, 8, 6, 8, 8, 9, 10, 12, 7, 7, 9, 9, 7, 10, 10, 9, 14, 11, 12, 9, 7, 13, 17, 2, 11, 12, 19, 15, 12, 10, 15, 15, 16, 19, 7, 7, 12

Offset: 0

Author

Cino Hilliard, Jan 31 2003

Keywords

• nonn
• base
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A079714.

Cf. A000142, A137579, A137580.

Cf. A316868.

Programs

Maple

a:= n-> numboccur(7, convert(n!, base, 10)):
seq(a(n), n=0..101);  # Alois P. Heinz, Apr 26 2021

PARI

a(n) = #select(x->(x==7), digits(n!)); \\ Michel Marcus, Apr 26 2021

Formula

a(n) = A034886(n) - (A027869(n) + A079680(n) + A079714(n) + A079684(n) + A079688(n) + A079690(n) + A079691(n) + A079693(n) + A079694(n)). - Reinhard Zumkeller, Jan 27 2008

Extensions

a(78)-a(79) corrected by Georg Fischer, Apr 26 2021