A130634 Additive persistence of double factorials.

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

Offset

0,7

Links

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

Example

10!! = 10*8*6*4*2 = 3840 -> 3+8+4+0 = 15 -> 1+5 = 6 -> persistence = 2.

Maple

with(numtheory): with(combinat): P:=proc(n) local a, t; t:=0; if n mod 2=0 then a:=2^(n/2)*(n/2)!; else a:=(n+1)!/(2^((n+1)/2)*((n+1)/2)!); fi;
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[Plus@@IntegerDigits[#]&, n!!, #>=10&]], {n, 0, 87}]-1 (* James C. McMahon, Feb 11 2025 *)

Crossrefs

Cf. A001147.

Sequence in context: A043568 A043543 A237684 * A274828 A364136 A257474

Adjacent sequences: A130631 A130632 A130633 * A130635 A130636 A130637

Keyword

easy,nonn,base

Author

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

Extensions

Corrected entries and Maple code by Paolo P. Lava, Dec 19 2017

Status

approved