A145279 Fecundity of n-th Fibonacci number.

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, 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, 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

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 06 2008

Keywords

• easy
• nonn
• base

Comments

Subset of A070562. After the 184th Fibonacci number 127127879743834334146972278486287885163, the fecundity is equal to zero.

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

Examples

			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.
		

Crossrefs

Cf. A070562, A145280.

Programs

Maple

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);

Mathematica

f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f@ Fibonacci@# &, 105, 0] (* Robert G. Wilson v, Jun 27 2010 *)