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%I #15 Aug 01 2015 12:17:35
%S 9,9,1,7,8,7,6,3,4,3,3,3,4,2,2,8,1,2,1,4,2,2,1,3,1,0,0,0,0,7,5,3,3,2,
%T 8,6,2,6,1,2,4,5,1,1,1,1,5,5,2,4,5,9,9,4,7,7,9,5,2,6,2,8,0,11,3,2,1,1,
%U 7,4,8,7,2,2,2,3,1,22,0,0,3,2,6,4,3,5,3,3,5,2,4,5,4,4,4,0,0,5,4,6,2,3,7,2,1
%N Fecundity of n-th prime.
%F a(n) = A070562(prime(n)). - _Michel Marcus_, Aug 01 2015
%e 7 -> 7+7=14 -> 14+1*4=18 -> 18+1*8=26 -> 26+2*6=38 -> 38+3*8=62 -> 62+6*2=74 -> 74+7*4=102 -> 7 steps to reach a zero digit.
%p P:=proc(i) local a,b,c,ok,k,w,n; for n from 1 by 1 to i do a:=ithprime(n); b:=1; c:=0; ok:=1; while ok=1 do k:=a; w:=1; while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w=0 then ok:=0; else c:=c+1; a:=a+w; fi; od; print(c); od; end: P(100);
%t f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f@Prime@# &, 105] (* _Robert G. Wilson v_, Jun 27 2010 *)
%Y Cf. A070562, A145279.
%K easy,nonn,base
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Oct 06 2008
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