S000756


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

S000756

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

© Tony D Noe 2014-2015