%N Primes p in prime triples (p, p+4, p+6) at the end of the maximal gaps in A201596.
%C Prime triples (p, p+4, p+6) are one of the two types of densest permissible constellations of 3 primes. Maximal gaps between triples of this type are listed in A201596; see more comments there.
%H Alexei Kourbatov, <a href="/A233435/b233435.txt">Table of n, a(n) for n = 1..79</a>
%H Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H Alexei Kourbatov, <a href="http://arxiv.org/abs/1309.4053">Tables of record gaps between prime constellations</a>, arXiv preprint arXiv:1309.4053, 2013.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e The gap of 6 between triples starting at p=7 and p=13 is the very first gap, so a(1)=13. The gap of 24 between triples starting at p=13 and p=37 is a maximal (record) gap - larger than any preceding gap; therefore a(2)=37. The gap of 30 between triples at p=37 and p=67 is again a record, so a(3)=67. The next gap is smaller, so a new term is not added to the sequence.
%Y Cf. A022005, A201596, A201597.
%A _Alexei Kourbatov_, Dec 09 2013