A091942 a(n) equals the maximum number of partial quotients in the simple continued fraction expansion of (1/n + 1/k) for k>=1.

2, 6, 7, 8, 9, 9, 11, 11, 12, 11, 12, 14, 13, 13, 13, 13, 14, 13, 13, 14, 15, 14, 14, 14, 14, 15, 14, 15, 15, 15, 16, 16, 16, 17, 15, 16, 16, 16, 17, 15, 17, 17, 17, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 16, 19, 17, 19, 18, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 18, 19, 18