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

0,2

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

Links

Table of n, a(n) for n=0..103.

Example

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.

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 *)

Crossrefs

Cf. A070562, A145280.

Sequence in context: A099401 A263450 A087028 * A103708 A239051 A131722

Adjacent sequences: A145276 A145277 A145278 * A145280 A145281 A145282

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 06 2008

Status

approved