The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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
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
Sequence in context: A056695 A342746 A287006 * A057987 A243165 A336993
KEYWORD
nonn
AUTHOR
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Mar 10 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 00:00 EDT 2024. Contains 372758 sequences. (Running on oeis4.)