English

Odd Fibbinary Numbers and the Golden Ratio

Combinatorics 2018-12-06 v1

Abstract

The fibbinary numbers are positive integers whose binary representation contains no consecutive ones. We prove the following result: If the jjth odd fibbinary is the nnth \emph{odd} fibbinary number, then j=nϕ21.j = \lfloor n\phi^2 \rfloor - 1.

Keywords

Cite

@article{arxiv.1812.02107,
  title  = {Odd Fibbinary Numbers and the Golden Ratio},
  author = {Linus Lindroos and Andrew Sills and Hua Wang},
  journal= {arXiv preprint arXiv:1812.02107},
  year   = {2018}
}

Comments

5 pages

R2 v1 2026-06-23T06:32:57.834Z