A079714 Number of 2's in n!.

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

Offset

0,14

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to factorial numbers.

Formula

a(n) = A034886(n) - (A027869(n) + A079680(n) + A079684(n) + A079688(n) + A079690(n) + A079691(n) + A079692(n) + A079693(n) + A079694(n)). - Reinhard Zumkeller, Jan 27 2008

Maple

a:= n-> numboccur(2, convert(n!, base, 10)):
seq(a(n), n=0..101);  # Alois P. Heinz, Apr 26 2021

Mathematica

Table[DigitCount[n!, 10, 2], {n, 0, 110}] (* Harvey P. Dale, Jun 20 2021 *)

Prog

(PARI) a(n) = #select(x->(x==2), digits(n!)); \\ Michel Marcus, Apr 26 2021

Crossrefs

Cf. A000142, A137579, A137580.

Cf. A316863.

Sequence in context: A273528 A085080 A260308 * A286889 A286368 A190710

Adjacent sequences: A079711 A079712 A079713 * A079715 A079716 A079717

Keyword

nonn,base,easy

Author

Cino Hilliard, Jan 31 2003

Extensions

a(36) ff. corrected by Georg Fischer, Apr 26 2021

Status

approved