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A233426 Primes p in prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) at the end of the maximal gaps in A200503.

%I A233426 #12 Feb 16 2025 08:33:21
%S A233426 97,16057,43777,1091257,6005887,14520547,40660717,87423097,94752727,
%T A233426 112710877,403629757,1593658597,2057241997,5933145847,6860027887,
%U A233426 14112464617,23504713147,24720149677,29715350377,29952516817,45645253597,53086708387,58528934197,93495691687,97367556817
%N A233426 Primes p in prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) at the end of the maximal gaps in A200503.
%C A233426 Prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) are densest permissible constellations of 6 primes. Maximal (record) gaps between prime sextuplets are listed in A200503; see further comments there.
%H A233426 Alexei Kourbatov, <a href="/A233426/b233426.txt">Table of n, a(n) for n = 1..56</a>
%H A233426 Tony Forbes and Norman Luhn, <a href="https://pzktupel.de/ktuplets.php">Prime k-tuplets</a>
%H A233426 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm#6tuples">Maximal gaps between prime k-tuples</a>
%H A233426 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 A233426 Norman Luhn, <a href="https://pzktupel.de/RecordGaps/GAP06.php">Record Gaps Between Prime Sextuplets</a>
%H A233426 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%F A233426 a(n) = A200504(n) + A200503(n). - _Hugo Pfoertner_, May 21 2023
%e A233426 Two smallest prime sextuplets (p, p+4, p+6, p+10, p+12, p+16) start at p=7 and p=97; so a[1]=97. The gap of 15960 between sextuplets starting at p=97 and p=16057 is a record gap - larger than any preceding gap; so a[2]=16057. The next gap is not a record, so a new term is not added.
%Y A233426 Cf. A022008, A200503, A200504.
%K A233426 nonn
%O A233426 1,1
%A A233426 _Alexei Kourbatov_, Dec 09 2013