A233425 - OEIS

%I #7 Dec 10 2013 12:28:10

%S 165701,1068701,11900501,39431921,67816361,124716071,300768311,

%T 428319371,661972301,1346761511,1699221521,3205239881,10540522241,

%U 16206106991,23911479071,38749334621,159330579041,351146640191,383960791211,714031248641,2881987944371,3381911721101,5105053487531

%N Primes p in prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20) at the end of the maximal gaps in A201051.

%C Prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20) are one of the two types of densest permissible constellations of 7 primes. Maximal gaps between septuplets of this type are listed in A201051; see more comments there.

%H Alexei Kourbatov, <a href="/A233425/b233425.txt">Table of n, a(n) for n = 1..36</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/maximalgapsbetweenprimeseptuplets.htm">Maximal gaps between prime septuplets</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 W. Weisstein, <a href="http://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>

%e The gap of 165690 between septuplets starting at p=11 and p=165701 is the very first gap, so a(1)=165701. The gap of 903000 between septuplets starting at p=165701 and p=1068701 is a maximal (record) gap - larger than any preceding gap; therefore a(2)=1068701. The next gap of 10831800 ending at p=11900501 is again a record, so a(3)=11900501. The next gap is smaller, so a new term is not added to the sequence.

%Y Cf. A022009, A201051, A201249.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Dec 09 2013