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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
1, 2, 3, 5, 8, 12, 13, 17, 19, 20, 21, 25, 27, 28, 30, 31, 32, 34, 38, 40, 41, 43, 44, 45, 48, 49, 50, 52, 55, 59, 61, 62, 64, 65, 66, 69, 70, 71, 73, 77, 78, 79, 81, 84, 88, 89, 93, 95, 96, 98, 99, 100, 103, 104, 105, 107, 111, 112, 113, 115, 118, 122, 124, 125
OFFSET
1,2
COMMENTS
Numbers k such that A095076(k) = 1. - Amiram Eldar, Feb 05 2023
REFERENCES
C. G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci, Simon Stevin 29 (1952), 190-195.
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.
LINKS
D. E. Daykin, Representation of natural numbers as sums of generalized Fibonacci numbers, J. London Math. Soc. 35 (1960), 143-160.
FORMULA
A007895(a(n)) mod 2 = 1. - Reinhard Zumkeller, Mar 10 2013
MATHEMATICA
Flatten @ Position[Mod[DigitCount[Select[Range[0, 1000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1] - 1 (* Amiram Eldar, Feb 05 2023 *)
PROG
(Haskell)
a020899 n = a020899_list !! (n-1)
a020899_list = filter (odd . a007895) [1..]
-- Reinhard Zumkeller, Mar 10 2013
CROSSREFS
KEYWORD
nonn
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Mar 10 2013
STATUS
approved