A205725 (prime(k)-prime(j))/10, where the pairs (k,j) are given by A205720 and A205721.

1, 1, 2, 1, 1, 2, 3, 2, 3, 1, 4, 3, 2, 4, 3, 1, 5, 4, 3, 1, 4, 3, 5, 3, 2, 6, 5, 3, 2, 6, 4, 3, 1, 7, 6, 5, 3, 2, 6, 5, 2, 8, 7, 6, 4, 3, 1, 7, 6, 3, 1, 9, 8, 6, 5, 3, 9, 7, 6, 4, 3, 10, 9, 8, 6, 5, 3, 2, 10, 9