A103934 Choose a(n) to be the smallest odd number not yet used such that: a(1) = 1, a(2n) = prime, a(2n+1) = composite and partial sums are alternately composite or prime.
1, 3, 9, 5, 25, 7, 21, 11, 15, 13, 27, 17, 39, 19, 45, 23, 33, 29, 55, 31, 35, 37, 57, 41, 49, 43, 119, 47, 51, 53, 91, 59, 77, 61, 125, 67, 143, 71, 69, 73, 65, 79, 63, 83, 75, 89, 121, 97, 81, 101, 99, 103, 87, 107, 117, 109, 135, 113, 93, 127, 111, 131, 129, 137, 115, 139
Offset: 1