A086517 a(1) = 1 and then the smallest odd number not included earlier such that the arithmetic mean of a pair of successive terms is prime.

1, 3, 7, 15, 11, 23, 35, 27, 19, 39, 43, 31, 51, 55, 63, 59, 47, 71, 75, 67, 79, 87, 91, 103, 99, 95, 83, 111, 107, 119, 135, 127, 147, 115, 139, 123, 131, 143, 155, 159, 167, 179, 183, 151, 163, 171, 175, 187, 195, 191, 203, 219, 227, 231, 215, 207, 239, 243, 211