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%I #20 Jan 19 2019 04:14:58
%S 5,17,41,107,347,461,881,1607,2267,2687,6197,6827,39227,46181,56891,
%T 83267,167621,375251,381527,549161,741677,805031,931571,2095361,
%U 2428451,4769111,4938287,12300641,12652457,13430171,14094797,18074027,29480651,107379731,138778301,156377861
%N Initial primes in prime triples (p, p+2, p+6) preceding the maximal gaps in A201598.
%C Prime triples (p, p+2, 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 A201598; see more comments there.
%H Alexei Kourbatov, <a href="/A201599/b201599.txt">Table of n, a(n) for n = 1..72</a>
%H Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenprimetriplets.htm">Maximal gaps between prime triples</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 [math.NT], 2013.
%H Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
%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=5 and p=11 is the very first gap, so a(1)=5. The gap of 6 between triples starting at p=11 and p=17 is not a record, so it does not contribute to the sequence. The gap of 24 between triples starting at p=17 and p=41 is a maximal gap - larger than any preceding gap; therefore a(2)=17.
%Y Cf. A022004 (prime triples p, p+2, p+6), A201598.
%K nonn
%O 1,1
%A _Alexei Kourbatov_, Dec 03 2011
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