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A130631 Multiplicative persistence of Fibonacci numbers. 0

%I #4 Aug 24 2012 10:49:59

%S 0,0,0,0,0,0,0,1,1,2,3,3,2,2,4,1,2,3,2,2,2,1,4,2,3,1,3,3,4,2,1,3,1,2,

%T 1,2,1,2,1,2,1,1,3,3,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,3,1,2,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1

%N Multiplicative persistence of Fibonacci numbers.

%C From the 184th terms on all the Fibonacci numbers have same digits equal to zero thus the persistence is equal to 1.

%e 3524578 -> 3*5*2*4*5*7*8 = 33600 -> 3*3*6*0*0 = 0 -> persistence = 2.

%p P:=proc(n)local f0,f1,f2,i,k,w,ok,cont; f0:=0; f1:=1; print(0); print(0); for i from 0 by 1 to n do f2:=f1+f0; f0:=f1; f1:=f2; w:=1; ok:=1; k:=f2; 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. A000045.

%K easy,nonn,base

%O 0,10

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 19 2007

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