A165276 - OEIS

%I #9 Jan 20 2020 13:01:48

%S 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,

%T 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,

%U 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

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

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

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

%H Amiram Eldar, <a href="/A165276/b165276.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%Y Cf. A014417, A165277, A165278, A165279.

%K nonn

%O 1,4

%A _Clark Kimberling_, Sep 12 2009