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A130543
Multiplicative persistence of n!.
2
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,1
COMMENTS
From 5! on all the factorials end with "zero" thus the persistence is equal to 1.
Decimal expansion of 1/90000. - Elmo R. Oliveira, May 05 2024
FORMULA
From Elmo R. Oliveira, Jul 16 2024: (Start)
G.f.: x^4/(1-x).
a(n) = 1 for n >= 4.
a(n) = 1 - A329678(n) = A185115(n+1). (End)
EXAMPLE
0!=1; 1!=1; 2!=2; 3!=6 --> Persistence=0
4!=24 --> 2*4=8 --> Persistence=1
5!=120 --> 1*2*0=0 --> Persistence=1
MAPLE
P:=proc(n)local i, k, w, ok, cont; for i from 0 by 1 to n do w:=1; k:=i!; ok:=1; if k<10 then print(0); else cont:=1; while ok=1 do while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w<10 then ok:=0; print(cont); else cont:=cont+1; k:=w; w:=1; fi; od; fi; od; end: P(100);
CROSSREFS
KEYWORD
easy,base,nonn
AUTHOR
STATUS
approved