English

Carmichael numbers in the sequence (k2^n+1)_{n\ge 1}

Number Theory 2013-05-16 v1

Abstract

We prove that for each odd number k, the sequence (k2^n+1)_{n\ge 1} contains only a finite number of Carmichael numbers. We also prove that k=27 is the smallest value for which such a sequence contains some Carmichael number.

Keywords

Cite

@article{arxiv.1305.3580,
  title  = {Carmichael numbers in the sequence (k2^n+1)_{n\ge 1}},
  author = {Javer Cilleruelo and Florian Luca and Amalia Pizarro},
  journal= {arXiv preprint arXiv:1305.3580},
  year   = {2013}
}

Comments

25 pages

R2 v1 2026-06-22T00:17:10.291Z