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A165277
Number of odd-indexed Fibonacci numbers in the Zeckendorf representation of n.
6
0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2
OFFSET
1,7
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 even-indexed Fibonacci summands, see A165276.
LINKS
EXAMPLE
6 = 5 + 1 = F(5) + F(2), so that a(6) = 1.
MATHEMATICA
fibOddCount[n_] := Plus @@ (Reverse@IntegerDigits[n, 2])[[2 ;; -1 ;; 2]]; fibOddCount /@ Select[Range[1000], BitAnd[#, 2 #] == 0 &] (* Amiram Eldar, Jan 20 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 12 2009
STATUS
approved