A129896 a(1)=1. a(n) = a(n-1) + number of Fibonacci numbers among the first (n-1) terms of the sequence.

1, 2, 4, 6, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209

Offset

1,2

Comments

The Fibonacci numbers in this sequence are: 1, 2, 8, 89, 233, 46368, 14930352, ..., . (A131349) - Robert G. Wilson v, Jul 02 2007

Links

Table of n, a(n) for n=1..62.

Mathematica

fibQ[n_] := (Fibonacci@ Round@ Log[ GoldenRatio, n*Sqrt@5] == n); f[lst_] := Append[lst, Last@lst + Length@Select[lst, fibQ@# &]]; Nest[f, {1}, 38] (* Robert G. Wilson v, Jul 02 2007 *)
nxt[{fibs_, a_}]:=Module[{f=Fibonacci[Range[50]], x=fibs}, If[MemberQ[f, a], x++]; {x, a+x}]; NestList[nxt, {0, 1}, 70][[All, 2]] (* Harvey P. Dale, Sep 16 2020 *)

Crossrefs

Sequence in context: A331417 A077473 A200738 * A134421 A092777 A186380

Adjacent sequences: A129893 A129894 A129895 * A129897 A129898 A129899

Keyword

nonn

Author

Leroy Quet, Jun 04 2007

Extensions

More terms from Robert G. Wilson v, Jul 02 2007

Status

approved