Journal of Integer Sequences, Vol. 19 (2016), Article 16.2.3

Generalized Multiple Counting Jacobsthal Sequences of Fermat Pseudoprimes

M. Hüsrev Cılasun
Emerging Circuits and Computation Group
Electrical and Electronics Faculty
Istanbul Technical University
Maslak, Istanbul


This study involves definitions of regular and representational multiple-counting Jacobsthal sequences of Carmichael numbers. We introduce recurrence relations for multiple-counting Jacobsthal sequences and show their association with Fermat's little theorem. We also provide matrix representations and generalized Binet formulas for defined sequences. This leads to a better understanding of how certain composite numbers are distributed among consecutive powers.

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(Concerned with sequences A000302 A001045 A006880 A007910 A077947 A093138.)

Received September 26 2015; revised versions received October 23 2015; December 1 2015; December 19 2015. Published in Journal of Integer Sequences, January 10 2016.

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