For the lower twin primes in S000758, the total distance to the nearest primes.
3, 6, 8, 12, 16, 20, 30, 32, 34, 38, 40, 62, 66, 68, 70, 80, 88, 112, 140, 176, 196, 206, 218, 226, 262, 278, 300, 328
1
That is, the sum of distance from S000758(i) to the nearest smaller prime and S000758(i)+2 to the nearest larger 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][[2]]
nonn,more
T. D. Noe, Nov 26 2015