A165276 Number of even-indexed Fibonacci numbers in the Zeckendorf representation of n.

1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 4, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 4, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 2, 3, 4, 2, 3, 2, 3, 4, 3, 4, 5, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 0, 1

Offset

1,4

Comments

We begin the indexing at 2; that is, 1=F(2), 2=F(3), 3=F(4), 5=F(5), ...

For a count of odd-indexed Fibonacci summands, see A165277.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

6 = 5 + 1 = F(5) + F(2), so that a(6) = 1.

Mathematica

fibEvenCount[n_] := Plus @@ (Reverse@IntegerDigits[n, 2])[[1 ;; -1 ;; 2]]; fibEvenCount /@ Select[Range[1000], BitAnd[#, 2 #] == 0 &] (* Amiram Eldar, Jan 20 2020 *)

Crossrefs

Cf. A014417, A165277, A165278, A165279.

Sequence in context: A287104 A190483 A090239 * A035698 A230204 A325592

Adjacent sequences: A165273 A165274 A165275 * A165277 A165278 A165279

Keyword

nonn

Author

Clark Kimberling, Sep 12 2009

Status

approved