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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Carmichael numbers in the sequence $(2^n k+1)_{n\ge 1}$
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by Javier Cilleruelo, Florian Luca and Amalia Pizarro-Madariaga PDF
Math. Comp. 85 (2016), 357-377 Request permission


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.
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Additional Information
  • Javier Cilleruelo
  • Affiliation: Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) and Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, España
  • MR Author ID: 292544
  • Email:
  • Florian Luca
  • Affiliation: School of Mathematics, University of the Witwatersrand, P. O. Box Wits 2050, South Africa
  • MR Author ID: 630217
  • Email:
  • Amalia Pizarro-Madariaga
  • Affiliation: Instituto de Matemáticas, Universidad de Valparaiso, Chile
  • Email:
  • Received by editor(s): August 12, 2013
  • Received by editor(s) in revised form: July 22, 2014, and July 29, 2014
  • Published electronically: June 15, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 357-377
  • MSC (2010): Primary 11A51, 11J86, 11J87
  • DOI:
  • MathSciNet review: 3404453