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

0,1

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

Links

Table of n, a(n) for n=0..100.

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

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

Cf. A031346, A130544, A185115, A329678.

Sequence in context: A085137 A304577 A194670 * A185013 A346459 A193243

Adjacent sequences: A130540 A130541 A130542 * A130544 A130545 A130546

Keyword

easy,base,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 04 2007

Status

approved