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%I #11 Aug 01 2015 12:09:49
%S 0,10,10,9,9,1,7,7,5,2,1,3,1,5,8,0,5,2,1,3,1,0,1,1,7,0,2,3,3,5,0,1,0,
%T 5,0,1,0,5,0,1,0,0,1,2,0,0,0,0,0,0,0,0,0,5,2,1,3,5,1,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0
%N Fecundity of n-th Fibonacci number.
%C Subset of A070562. After the 184th Fibonacci number 127127879743834334146972278486287885163, the fecundity is equal to zero.
%C The indices of Fibonacci numbers whose fecundity is not zero are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 33, 35, 37, 39, 42, 43, 53, 54, 55, 56, 57, 58, 78, 80, 85, 87, 97, 125, 184}. - _Robert G. Wilson v_, Jun 27 2010
%e Fib(6)=8 -> 8+8=16 -> 16+1*6=22 -> 22+2*2=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,d,f,g,ok,k,w,n; d:=0; f:=1; print(d); print(10); for n from 0 by 1 to i do a:=d+f; g:=f; f:=a; d:=g; 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(200);
%t f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f@ Fibonacci@# &, 105, 0] (* _Robert G. Wilson v_, Jun 27 2010 *)
%Y Cf. A070562, A145280.
%K easy,nonn,base
%O 0,2
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Oct 06 2008
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