A138383 If p(i) = i-th prime, a(n) = p(n)+1 + p(n)+2 + ... + p(n+1). a(0) = 3 by convention.

3, 3, 9, 13, 38, 25, 62, 37, 86, 159, 61, 207, 158, 85, 182, 303, 339, 121, 387, 278, 145, 459, 326, 519, 748, 398, 205, 422, 217, 446, 1687, 518, 807, 277, 1445, 301, 927, 963, 662, 1023, 1059, 361, 1865, 385, 782, 397, 2466, 2610, 902, 457, 926, 1419, 481, 2465, 1527