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A130635
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Additive persistence of factorial numbers.
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0
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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
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OFFSET
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0,10
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LINKS
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EXAMPLE
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10! = 10*9*8*7*6*5*4*3*2 = 3628800 -> 3+6+2+8+8 = 27 -> 2+7 = 9 -> persistence = 2.
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MAPLE
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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);
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MATHEMATICA
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Table[Length[NestWhileList[Total[IntegerDigits[#]]&, n!, #>9&]]-1, {n, 0, 90}] (* Harvey P. Dale, Jul 19 2022 *)
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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Corrected entries and Maple code
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STATUS
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approved
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