a(n) = p is the smallest prime introducing a consecutive prime-difference pattern as follows: [2,2n,2], i.e., [p, p+2, p+2+2n, p+2+2n+2] are consecutive primes. Increasing middle prime gap in the immediate neighborhood of two small gaps(=2); a(n) = 0 if no such pattern exists.

A082512

a(n) = p is the smallest prime introducing a consecutive prime-difference pattern as follows: [2,2n,2], i.e., [p, p+2, p+2+2n, p+2+2n+2] are consecutive primes. Increasing middle prime gap in the immediate neighborhood of two small gaps(=2); a(n) = 0 if no such pattern exists.