A130635 Additive persistence of factorial numbers.

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3

Offset

0,10

Links

Table of n, a(n) for n=0..87.

Example

10! = 10*9*8*7*6*5*4*3*2 = 3628800 -> 3+6+2+8+8 = 27 -> 2+7 = 9 -> persistence = 2.

Maple

with(numtheory): with(combinat): P:=proc(n) local a, t; t:=0; a:=n!;
while a>9 do t:=t+1; a:=convert(convert(a, base, 10), `+`); od; t;
end: seq(P(i), i=0..10^2);

Mathematica

Table[Length[NestWhileList[Total[IntegerDigits[#]]&, n!, #>9&]]-1, {n, 0, 90}] (* Harvey P. Dale, Jul 19 2022 *)

Crossrefs

Cf. A000142.

Sequence in context: A177830 A111859 A156822 * A107609 A243113 A258198

Adjacent sequences: A130632 A130633 A130634 * A130636 A130637 A130638

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 19 2007, corrected Jun 22 2007

Extensions

Corrected entries and Maple code

Status

approved