## 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

## 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.## References

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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: franciscojavier.cilleruelo@uam.es
**Florian Luca**- Affiliation: School of Mathematics, University of the Witwatersrand, P. O. Box Wits 2050, South Africa
- MR Author ID: 630217
- Email: fluca@wits.ac.za
**Amalia Pizarro-Madariaga**- Affiliation: Instituto de Matemáticas, Universidad de Valparaiso, Chile
- Email: amalia.pizarro@uv.cl
- 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: https://doi.org/10.1090/mcom/2982
- MathSciNet review: 3404453