A049881 a(n)=number of distinct sums of 3 of the first n primes.

1, 4, 10, 16, 23, 30, 38, 47, 57, 67, 77, 87, 96, 106, 116, 129, 140, 151, 160, 172, 183, 194, 208, 220, 231, 242, 252, 261, 279, 292, 304, 319, 334, 346, 360, 374, 389, 400, 413, 426, 440, 452, 464, 476, 488, 505