A121217 a(1)=1, a(2)=2, a(3)=3; for n>3, a(n) = the smallest positive integer which does not occur earlier in the sequence and which is not coprime to a(n-2).

1, 2, 3, 4, 6, 8, 9, 10, 12, 5, 14, 15, 7, 18, 21, 16, 24, 20, 22, 25, 11, 30, 33, 26, 27, 13, 36, 39, 28, 42, 32, 34, 38, 17, 19, 51, 57, 45, 48, 35, 40, 49, 44, 56, 46, 50, 23, 52, 69, 54, 60, 58, 55, 29, 65, 87, 70, 63, 62, 66, 31, 64, 93, 68, 72, 74, 75, 37, 78, 111, 76, 81