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A020899
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Numbers k with an odd number of terms in their Zeckendorf representation (write k as a sum of non-consecutive distinct Fibonacci numbers).
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12
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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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.
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LINKS
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FORMULA
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MATHEMATICA
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Flatten @ Position[Mod[DigitCount[Select[Range[0, 1000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1] - 1 (* Amiram Eldar, Feb 05 2023 *)
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PROG
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(Haskell)
a020899 n = a020899_list !! (n-1)
a020899_list = filter (odd . a007895) [1..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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