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A113403 Primes p in prime quadruplets (p,p+2,p+6,p+8) at the end of maximal gaps in A113404.

%I A113403 #31 Feb 16 2025 08:32:59
%S A113403 11,101,821,1481,3251,5651,9431,31721,43781,97841,135461,187631,
%T A113403 326141,768191,1440581,1508621,3047411,3798071,5146481,5610461,
%U A113403 9020981,17301041,22030271,47774891,66885851,76562021,87797861,122231111,132842111,204651611,628641701,1749878981
%N A113403 Primes p in prime quadruplets (p,p+2,p+6,p+8) at the end of maximal gaps in A113404.
%C A113403 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 A113403 Jud McCranie and Alexei Kourbatov, <a href="/A113403/b113403.txt">Table of n, a(n) for n = 1..71</a>
%H A113403 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>.
%H A113403 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm#4tuples">Maximal gaps between prime k-tuples</a>.
%H A113403 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 A113403 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>.
%e A113403 Record gaps between prime quadruplets are as follows (arXiv:1309.4053, Table 4):
%e A113403 Initial primes: Max gap
%e A113403 .....5......11........6
%e A113403 ....11.....101.......90
%e A113403 ...191.....821......630
%e A113403 ...821....1481......660
%e A113403 ..2081....3251.....1170
%e A113403 ..3461....5651.....2190
%e A113403 ..5651....9431.....3780
%e A113403 ...
%e A113403 The left column is A229907. The middle column is A113403 (this sequence); the right column is A113404.
%Y A113403 Record gaps are given in A113404. Cf. A007530, A002386.
%K A113403 nonn
%O A113403 1,1
%A A113403 _Bernardo Boncompagni_, Oct 28 2005