A020899 - OEIS

A020899

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

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)

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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