Sequence of pairs (s1,s2) of the distance from a twin prime pair to the next lower and higher prime.
1, 2, 2, 4, 4, 4, 4, 4, 6, 6, 4, 4, 6, 6, 4, 6, 4, 4, 4, 4, 6, 10, 10, 6, 6, 10, 10, 4, 4, 12, 4, 4, 6, 10, 6, 6, 4, 10, 4, 4, 10, 4, 10, 10, 10, 6, 4, 4, 12, 18, 6, 6, 6, 6, 4, 12, 10, 4, 6, 12, 12, 10, 10, 4, 4, 10, 4, 4, 4, 4, 6, 10, 10, 6, 10, 10, 10, 6
1
That is, given a prime pair {p1,p2), with p2 = p1 + 2, p1-s1 is the next lower prime and p2+s2 is the next higher prime.
T. D. Noe, Plot of 5000 pairs
T. D. Noe, Table of 5000 pairs
Eric W. Weisstein, MathWorld: Twin Primes
(Mma) tp = Select[Prime[Range[200]], PrimeQ[# + 2] &]; t = Table[{tp[[n]] - Prime[PrimePi[tp[[n]]] - 1], Prime[PrimePi[tp[[n]] + 2] + 1] - tp[[n]] - 2}, {n, Length[tp]}]; Flatten[t]
Cf. A001097 (twin primes).
nonn
T. D. Noe, Nov 22 2015