Smallest number at distance 3n from nearest prime.

[Jonathan Post]

Smallest number at distance 3n from nearest prime.

2, 0, 119, 896, 1339, 1342, ...

offset 0,1

Formula: a(n) = MIN{k such that |k-p| = 3n for some p = prime(j), and
|k-prime(j+1)| =>3n}.

Comment: analogue of A051728 which uses 2n. "Prime" is restricted to
positive integers. Largest number less than the mean of the smallest
prime gap of size at least 6n.

Examples:

a(0) = 2 because |2-0| = 2 and there are no primes < 2.
a(1) = 0 because |0-3| = 3 and there are no primes < 0.
a(2) = 119 because |119-113| = 6 and |119-127| = 8.
a(3) = 896 because |896-887| = 9 and |896-907| = 11.

This is the 3rd row of an array whose first row is A000040, and second
row is A051728.  Is it interesting to code this, and show the next few
rows, perhaps by showing the array by antidiagonals?