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 A165276 #9 Jan 20 2020 13:01:48 %S A165276 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 A165276 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 A165276 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 A165276 Number of even-indexed Fibonacci numbers in the Zeckendorf representation of n. %C A165276 We begin the indexing at 2; that is, 1=F(2), 2=F(3), 3=F(4), 5=F(5), ... %C A165276 For a count of odd-indexed Fibonacci summands, see A165277. %H A165276 Amiram Eldar, <a href="/A165276/b165276.txt">Table of n, a(n) for n = 1..10000</a> %e A165276 6 = 5 + 1 = F(5) + F(2), so that a(6) = 1. %t A165276 fibEvenCount[n_] := Plus @@ (Reverse@IntegerDigits[n, 2])[[1 ;; -1 ;; 2]]; fibEvenCount /@ Select[Range[1000], BitAnd[#, 2 #] == 0 &] (* _Amiram Eldar_, Jan 20 2020 *) %Y A165276 Cf. A014417, A165277, A165278, A165279. %K A165276 nonn %O A165276 1,4 %A A165276 _Clark Kimberling_, Sep 12 2009