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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). 12

%I

%S 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 48,49,50,52,55,59,61,62,64,65,66,69,70,71,73,77,78,79,81,84,88,89,93,

%U 95,96,98,99,100,103,104,105,107,111,112,113,115,118,122,124,125

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

%C Numbers k such that A095076(k) = 1. - _Amiram Eldar_, Feb 05 2023

%D C. G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci, Simon Stevin 29 (1952), 190-195.

%D Edouard Zeckendorf, Repr├ęsentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Li├Ęge 41 (1972), 179-182.

%H Reinhard Zumkeller, <a href="/A020899/b020899.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 A007895(a(n)) mod 2 = 1. - _Reinhard Zumkeller_, Mar 10 2013

%t Flatten @ Position[Mod[DigitCount[Select[Range[0, 1000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1] - 1 (* _Amiram Eldar_, Feb 05 2023 *)

%o (Haskell)

%o a020899 n = a020899_list !! (n-1)

%o a020899_list = filter (odd . a007895) [1..]

%o -- _Reinhard Zumkeller_, Mar 10 2013

%Y Cf. A007895, A014417, A095076.

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Offset corrected by _Reinhard Zumkeller_, Mar 10 2013

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Last modified April 1 19:13 EDT 2023. Contains 361695 sequences. (Running on oeis4.)