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A130544 Multiplicative persistence of n!!. 1

%I #5 Aug 24 2012 10:49:59

%S 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,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Multiplicative persistence of n!!.

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

%e 6!!= 6*4*2= 48 --> 4*8=32 --> 3*2= 6 --> Persistence=2

%e 13!!=135135 --> 1*3*5*1*3*5=225 -->2*2*5=20 --> 2*0=0 --> Persistence=3

%p 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);

%Y Cf. A031346, A130543.

%K easy,nonn,base

%O 0,7

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 04 2007

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