A051356 Start with 0, run through primes >=5, adding if -1 mod 6, subtracting if +1 mod 6.

0, 5, -2, 9, -4, 13, -6, 17, 46, 15, -22, 19, -24, 23, 76, 135, 74, 7, 78, 5, -74, 9, 98, 1, 102, -1, 106, -3, 110, -17, 114, 251, 112, 261, 110, -47, -210, -43, 130, 309, 128, 319, 126, 323, 124, -87, -310, -83, -312, -79, 160, -81, 170, 427, 690