New properties of a composition of ordinary generating functions for primes

Abstract

In this paper, we consider properties of coefficients of a composition of ordinary generating functions. Using the notion of a composita, we get some new properties for this composition. The obtained properties can be used for distinguishing prime numbers from composite numbers. As an application, the obtained results can be used for getting new primality criteria. For example, we show how to get primality criteria for the Mersenne numbers, the Lucas numbers, the Pell-Lucas numbers, the Jacobsthal-Lucas numbers, and other.

Subject Classification:

• 11Y11
• 11Y55
• 05A15

Keywords:

• Primality criterion
• integer sequence
• generating function
• composita