Let p and q be two prime numbers, not necessarily consecutive, such that q - p = 2n; then a(n) is the number of partitions of 2n into even numbers so that each partition corresponds to a consecutive prime difference pattern (k-tuple) and p <= A000230(n).

A079023

Let p and q be two prime numbers, not necessarily consecutive, such that q - p = 2n; then a(n) is the number of partitions of 2n into even numbers so that each partition corresponds to a consecutive prime difference pattern (k-tuple) and p <= A000230(n).