Least twin prime p2 such that there is a larger twin prime p1 with p1 - p2 = 2*n.

3, 3, 5, 3, 3, 5, 3, 3, 11, 11, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 17, 17, 13, 11, 11, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 29, 29, 31, 29, 29, 19, 17, 17, 13, 11, 11, 7, 5, 3, 3, 5, 3, 3, 29, 29, 199, 197, 197, 19, 17, 17, 13, 11, 11, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 29

1

This is the smaller twin prime required for S000945.

T. D. Noe, Plot of 10000 terms

T. D. Noe, Table of 10000 terms

Wikipedia, Twin prime

(Mma) prms = 100; tp = Select[Prime[Range[2, prms]], PrimeQ[# + 2] &]; tp = Union[tp, tp + 2]; u = Union[Select[Flatten[mat = Table[a - b, {a, tp}, {b, tp}]], # > 0 &]]; d = Differences[u]; mx = Position[d, _?(# > 2 &), 1, 1][[1, 1]]; nn = u[[mx]]/2; t = Table[0, {nn}]; n = 1; cnt = 0; While[cnt < nn, n++; diff = Reverse[Table[tp[[n]] - tp[[i]], {i, n - 1}]/2]; Do[If[diff[[i]] <= nn && t[[diff[[i]]]] == 0, cnt++; t[[diff[[i]]]] = tp[[n]]], {i, n - 1}]]; t - 2*Range[nn]

Cf. S000945.

nonn

T. D. Noe, Sep 29 2016