English

Consecutive Integers and the Collatz Conjecture

Number Theory 2015-12-01 v1

Abstract

Pairs of consecutive integers have the same height in the Collatz problem with surprising frequency. Garner gave a conjectural family of conditions for exactly when this occurs. Our main result is an infinite family of counterexamples to Garner's conjecture.

Keywords

Cite

@article{arxiv.1511.09141,
  title  = {Consecutive Integers and the Collatz Conjecture},
  author = {Marcus Elia and Amanda Tucker},
  journal= {arXiv preprint arXiv:1511.09141},
  year   = {2015}
}

Comments

Accepted at Integers, 9 pages

R2 v1 2026-06-22T11:56:55.008Z