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A201249 Initial primes in prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20) preceding the maximal gaps in A201051.

%I A201249 #11 Feb 16 2025 08:33:16
%S A201249 11,165701,1068701,25658441,45002591,93625991,257016491,367438061,
%T A201249 575226131,1228244651,1459270271,2923666841,10180589591,15821203241,
%U A201249 23393094071,37846533071,158303571521,350060308511,382631592641,711854781551,2879574595811,3379186846151
%N A201249 Initial primes in prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20) preceding the maximal gaps in A201051.
%C A201249 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 A201249 Alexei Kourbatov, <a href="/A201249/b201249.txt">Table of n, a(n) for n = 1..36</a>
%H A201249 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H A201249 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenprimeseptuplets.htm">Maximal gaps between prime septuplets</a>
%H A201249 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 A201249 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e A201249 The gap of 165690 between septuplets starting at p=11 and p=165701 is the very first gap, so a(1)=11. The gap of 903000 between septuplets starting at p=165701 and p=1068701 is a maximal gap - larger than any preceding gap; therefore a(2)=165701. The next gap of 10831800 starts at p=1068701 and is again a maximal gap, so a(3)=1068701. The next gap is smaller, so it does not contribute to the sequence.
%Y A201249 Cf. A022009 (prime septuplets p, p+2, p+6, p+8, p+12, p+18, p+20), A201051, A233425.
%K A201249 nonn,hard
%O A201249 1,1
%A A201249 _Alexei Kourbatov_, Nov 28 2011