For the lower twin primes in S000758, the distance to the nearest larger prime + 2.
2, 4, 4, 6, 10, 10, 18, 10, 16, 22, 18, 28, 36, 16, 18, 58, 54, 42, 100, 118, 108, 70, 40, 30, 138, 196, 54, 124
1
That is, the distance from the upper twin prime to the next prime.
T. D. Noe, Plot of 28 terms
Eric W. Weisstein, MathWorld: Twin Primes
(Mma) tp = Reap[Do[p = Prime[i]; If[PrimeQ[p + 2], Sow[p]], {i, PrimePi[2000000]}]][[2, 1]]; t = {{3, 3, 1, 2}}; Do[s = {tp[[n]] - Prime[PrimePi[tp[[n]]] - 1], Prime[PrimePi[tp[[n]] + 2] + 1] - tp[[n]] - 2}; If[s[[1]] + s[[2]] > t[[-1, 2]], AppendTo[t, {tp[[n]], s[[1]] + s[[2]], s[[1]], s[[2]]}]], {n, Length[tp]}]; Transpose[t][[4]]
nonn,more
T. D. Noe, Nov 26 2015