Journal of Generalized Lie Theory and Applications

On the Consecutive Integers n+i-1=(i+1) P_i

Abstract

Jiang CX

By using the Jiang’s function J₂ (ω) we prove that there exist infinitely many integers n such that n=2P₁, n+1=3P₂, n+k−1=(k+1) P_k are all composites for arbitrarily long k, where P₁, P₂,…, P_k are all primes. This result has no prior occurrence in the history of number theory.