%I #30 Sep 14 2021 15:08:55

%S 11,101,821,1481,3251,5651,9431,31721,43781,97841,135461,187631,

%T 326141,768191,1440581,1508621,3047411,3798071,5146481,5610461,

%U 9020981,17301041,22030271,47774891,66885851,76562021,87797861,122231111,132842111,204651611,628641701,1749878981

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

%C 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 Jud McCranie and Alexei Kourbatov, <a href="/A113403/b113403.txt">Table of n, a(n) for n = 1..71</a>

%H Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>.

%H Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm#4tuples">Maximal gaps between prime k-tuples</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 Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>.

%e Record gaps between prime quadruplets are as follows (arXiv:1309.4053, Table 4):

%e Initial primes: Max gap

%e .....5......11........6

%e ....11.....101.......90

%e ...191.....821......630

%e ...821....1481......660

%e ..2081....3251.....1170

%e ..3461....5651.....2190

%e ..5651....9431.....3780

%e ...

%e The left column is A229907. The middle column is A113403 (this sequence); the right column is A113404.

%Y Record gaps are given in A113404. Cf. A007530, A002386.

%K nonn

%O 1,1

%A _Bernardo Boncompagni_, Oct 28 2005