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A229907 Initial primes in prime quadruplets (p, p+2, p+6, p+8) preceding the maximal gaps in A113404.

%I A229907 #17 Feb 16 2025 08:33:20
%S A229907 5,11,191,821,2081,3461,5651,25301,34841,88811,122201,171161,301991,
%T A229907 739391,1410971,1468631,2990831,3741161,5074871,5527001,8926451,
%U A229907 17186591,21872441,47615831,66714671,76384661,87607361,122033201,132574061,204335771
%N A229907 Initial primes in prime quadruplets (p, p+2, p+6, p+8) preceding the maximal gaps in A113404.
%C A229907 Prime quadruplets (p, p+2, p+6, p+8) are densest permissible constellations of four primes. Record (maximal) gaps between prime quadruplets are listed in A113404; see further comments there.
%H A229907 Alexei Kourbatov, <a href="/A229907/b229907.txt">Table of n, a(n) for n = 1..71</a>
%H A229907 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H A229907 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm#4tuples">Maximal gaps between prime k-tuples</a>
%H A229907 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 A229907 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 A229907 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e A229907 Record gaps between prime quadruplets are as follows (arXiv:1309.4053, Table 4):
%e A229907 Initial primes: Max gap
%e A229907 .....5......11........6
%e A229907 ....11.....101.......90
%e A229907 ...191.....821......630
%e A229907 ...821....1481......660
%e A229907 ..2081....3251.....1170
%e A229907 ..3461....5651.....2190
%e A229907 ..5651....9431.....3780
%e A229907 ...
%e A229907 The left column is this sequence (A229907). The middle column is A113403; the right column is A113404.
%Y A229907 Cf. A007530, A113403, A113404.
%K A229907 nonn
%O A229907 1,1
%A A229907 _Alexei Kourbatov_, Dec 19 2013