A073883 a(1)=1. For n>1, a(n) = the smallest positive integer not included earlier such that the n-th partial sum is n times a prime.

1, 3, 2, 6, 13, 5, 19, 7, 43, 11, 33, 61, 17, 45, 79, 23, 125, 29, 67, 31, 157, 37, 129, 41, 91, 147, 47, 215, 53, 233, 59, 123, 259, 203, 71, 143, 73, 301, 235, 83, 329, 89, 433, 97, 277, 101, 195, 103, 299, 107, 209, 109, 321, 113, 883, 127, 355, 131, 485, 137