login
A165276
Number of even-indexed Fibonacci numbers in the Zeckendorf representation of n.
7
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 12 2009
STATUS
approved