A130544 Multiplicative persistence of n!!.

0, 0, 0, 0, 0, 1, 2, 1, 4, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 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
• nonn
• base

Comments

From 24!! on all the numbers have same digits equal to zero thus the persistence is equal to 1.

Examples

			6!!= 6*4*2= 48 --> 4*8=32 --> 3*2= 6 --> Persistence=2
13!!=135135 --> 1*3*5*1*3*5=225 -->2*2*5=20 --> 2*0=0 --> Persistence=3
		

Links

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

Crossrefs

Cf. A031346, A130543.

Programs

Maple

P:=proc(n) local i,k,w,ok,cont; for i from 0 by 1 to n do k:=i; w:=i-2; while w>0 do k:=k*w; w:=w-2; od; w:=1; 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);