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

Javer Cilleruelo, Florian Luca, Amalia Pizarro

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 suc…