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A130635
Additive persistence of factorial numbers.
0
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
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
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