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%I #3 Aug 24 2012 10:49:59
%S 0,0,0,0,1,1,1,3,1,5,4,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,
%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 Catalan numbers.
%C After the 57th terms all the numbers have some digits equal to zero thus the persistence is equal to 1.
%e Catalan number 429 -> 4*2*9=72 -> 7*2=14 -> 1*4=4 thus persistence is 3
%p P:=proc(n) local i,k,w,ok,cont; for i from 0 by 1 to n do k:=(2*i)!/(i!*(i+1)!); 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. A003001, A006050, A000108.
%K easy,nonn,base
%O 0,8
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 18 2007
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