This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165277 #12 Jan 20 2020 14:44:32 %S A165277 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, %T A165277 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, %U A165277 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 %N A165277 Number of odd-indexed Fibonacci numbers in the Zeckendorf representation of n. %C A165277 We begin the indexing at 2; that is, 1=F(2), 2=F(3), 3=F(4), 5=F(5), ... %C A165277 For a count of even-indexed Fibonacci summands, see A165276. %H A165277 Amiram Eldar, <a href="/A165277/b165277.txt">Table of n, a(n) for n = 1..10000</a> %e A165277 6 = 5 + 1 = F(5) + F(2), so that a(6) = 1. %t A165277 fibOddCount[n_] := Plus @@ (Reverse@IntegerDigits[n, 2])[[2 ;; -1 ;; 2]]; fibOddCount /@ Select[Range[1000], BitAnd[#, 2 #] == 0 &] (* _Amiram Eldar_, Jan 20 2020 *) %Y A165277 Cf. A014417, A165276, A165278, A165279. %K A165277 nonn %O A165277 1,7 %A A165277 _Clark Kimberling_, Sep 12 2009