In this paper, we will firstly define a new generalization of numbers (p, q) and then derive the appropriate Binet's formula generating functions concerning (p,q)-Fibonacci numbers, (p,q)- Lucas (p,q)-Pell (p,q)-Jacobsthal numbers. Also, some useful are provided for products (p,q)-numbers with bivariate complex Fibonacci polynomials.

Let j(n) denote the smallest positive integer m such that every sequence of m consecutive integers contains an integer prime to n. Let Pn be the product of the first n primes and define h(n) = j(Pn). Presently, h(n) is only known for n ≤ 24. In this paper, we describe an algorithm that enabled the calculation of h(n) for n < 50. 0.