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6n-1,6n+1, 6n+5, 6n+7 are all primes. That is they are adjacent pairs of twin primes.
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%I #7 Nov 21 2013 12:50:04

%S 1,2,17,32,137,247,312,347,542,577,942,1572,2167,2607,2622,2677,3007,

%T 3152,3237,3502,3712,4217,5287,5807,7297,8557,9222,10497,11202,11582,

%U 12037,12877,13282,13507,13787,14802,16307,16522,16852,18307,19422

%N 6n-1,6n+1, 6n+5, 6n+7 are all primes. That is they are adjacent pairs of twin primes.

%C The sequence A002822, gives the values of n to generate the twin primes, 6n+/-1. It has the values 1, 2, 3, 5, 7, 10, 12, 17, 18, 23, . This new sequence lists the lower of the values of this which are adjacent, namely 1(&2), 2 (&3), 17 (&18)..

%H Harvey P. Dale, <a href="/A178145/b178145.txt">Table of n, a(n) for n = 1..1000</a>

%t (First[#]+1)/6&/@Select[Partition[Prime[Range[12000]],4,1], Differences[#] == {2,4,2}&] (* _Harvey P. Dale_, Jan 23 2012 *)

%Y Cf. A002822

%K nonn

%O 1,2

%A _Anthony C Robin_, May 21 2010

%E Extended by _D. S. McNeil_, May 23 2010