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A020899 Numbers k with an odd number of terms in their Zeckendorf representation (write k as a sum of non-consecutive distinct Fibonacci numbers).

%I A020899 #20 Feb 05 2023 09:24:37
%S A020899 1,2,3,5,8,12,13,17,19,20,21,25,27,28,30,31,32,34,38,40,41,43,44,45,
%T A020899 48,49,50,52,55,59,61,62,64,65,66,69,70,71,73,77,78,79,81,84,88,89,93,
%U A020899 95,96,98,99,100,103,104,105,107,111,112,113,115,118,122,124,125
%N A020899 Numbers k with an odd number of terms in their Zeckendorf representation (write k as a sum of non-consecutive distinct Fibonacci numbers).
%C A020899 Numbers k such that A095076(k) = 1. - _Amiram Eldar_, Feb 05 2023
%D A020899 C. G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci, Simon Stevin 29 (1952), 190-195.
%D A020899 Edouard Zeckendorf, Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41 (1972), 179-182.
%H A020899 Reinhard Zumkeller, <a href="/A020899/b020899.txt">Table of n, a(n) for n = 1..10000</a>
%H A020899 D. E. Daykin, <a href="https://doi.org/10.1112/jlms/s1-35.2.143">Representation of natural numbers as sums of generalized Fibonacci numbers</a>, J. London Math. Soc. 35 (1960), 143-160.
%F A020899 A007895(a(n)) mod 2 = 1. - _Reinhard Zumkeller_, Mar 10 2013
%t A020899 Flatten @ Position[Mod[DigitCount[Select[Range[0, 1000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1] - 1 (* _Amiram Eldar_, Feb 05 2023 *)
%o A020899 (Haskell)
%o A020899 a020899 n = a020899_list !! (n-1)
%o A020899 a020899_list = filter (odd . a007895) [1..]
%o A020899 -- _Reinhard Zumkeller_, Mar 10 2013
%Y A020899 Cf. A007895, A014417, A095076.
%K A020899 nonn
%O A020899 1,2
%A A020899 _Clark Kimberling_
%E A020899 Offset corrected by _Reinhard Zumkeller_, Mar 10 2013