A103824 Choose a(n) to be the smallest 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, 2, 4, 5, 35, 7, 65, 11, 15, 13, 21, 17, 25, 19, 55, 23, 49, 29, 91, 31, 27, 37, 115, 41, 77, 43, 121, 47, 85, 53, 125, 59, 39, 61, 33, 67, 133, 71, 143, 73, 119, 79, 95, 83, 81, 89, 145, 97, 51, 101, 99, 103, 45, 107, 57, 109, 87, 113, 69, 127, 75, 131, 111, 137