Next prime after A000230(n).
3, 5, 11, 29, 97, 149, 211, 127, 1847, 541, 907, 1151, 1693, 2503, 2999, 4327, 5623, 1361, 9587, 30631, 19373, 16183, 15727, 81509, 28277, 31957, 19661, 35671, 82129, 44351, 43391, 34123, 89753, 162209, 134581, 173429, 31469, 404671, 212777, 188107, 542683
1
The prime at the end of the first gap of length A004277(n). Alternatively, s(n) = A000230(n) + A004277(n).
T. D. Noe, Plot of 120 terms
T. D. Noe, Table of 120 terms
Wen Huang and XiaoSheng Wu, A property on the difference of primes, arXiv 1505.00187 (Apr 28 2015)
(Mma) nn = 40; t = Table[0, {nn}]; p = 3; found = 0; While[found < nn, nextP = NextPrime[p]; diff = (nextP - p)/2; If[diff <= nn && t[[diff]] == 0, t[[diff]] = p; found++]; p = nextP]; t = Join[{2}, t]; NextPrime[t]
nonn
T. D. Noe, May 04 2015