For the lower twin primes in S000758, the distance to the nearest smaller prime.
1, 2, 4, 6, 6, 10, 12, 22, 18, 16, 22, 34, 30, 52, 52, 22, 34, 70, 40, 58, 88, 136, 178, 196, 124, 82, 246, 204
1
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][[3]]
nonn,more
T. D. Noe, Nov 26 2015