A130543 Multiplicative persistence of n!.

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

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007

Keywords

• easy
• base
• nonn

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

Examples

			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
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A031346, A130544, A185115, A329678.

Programs

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);

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)