Summary: 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.

11Bxx, 11Y55, 11A15

Carmichael number, Fermat's little theorem, binet formula, floor function, multiple-counting sequence, Fermat pseudoprime, Jacobsthal sequence