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A201252 Initial primes in prime septuplets (p, p+2, p+8, p+12, p+14, p+18, p+20) preceding the maximal gaps in A201251.

%I A201252 #16 Feb 16 2025 08:33:16
%S A201252 5639,88799,284729,1146779,8573429,24001709,43534019,87988709,
%T A201252 157131419,522911099,706620359,1590008669,2346221399,3357195209,
%U A201252 11768282159,30717348029,33788417009,62923039169,68673910169,88850237459,163288980299,196782371699,421204876439
%N A201252 Initial primes in prime septuplets (p, p+2, p+8, p+12, p+14, p+18, p+20) preceding the maximal gaps in A201251.
%C A201252 Prime septuplets (p, p+2, p+8, p+12, p+14, 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 A201251; see more comments there. A233038 lists the corresponding primes at the end of the maximal gaps.
%H A201252 Alexei Kourbatov, <a href="/A201252/b201252.txt">Table of n, a(n) for n = 1..52</a>
%H A201252 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H A201252 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenktuples.htm">Maximal gaps between prime k-tuples</a>
%H A201252 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 A201252 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e A201252 The gap of 83160 between septuplets starting at p=5639 and p=88799 is the very first gap, so a(1)=5639. The gap of 195930 between septuplets starting at p=88799 and p=284729 is a maximal gap - larger than any preceding gap; therefore a(2)=88799. The next gap starts at p=284729 and is again a maximal gap, so a(3)=284729. The next gap is smaller, so it does not contribute to the sequence.
%Y A201252 Cf. A022010 (prime septuplets p, p+2, p+8, p+12, p+14, p+18, p+20), A201251, A233038.
%K A201252 nonn,hard
%O A201252 1,1
%A A201252 _Alexei Kourbatov_, Nov 28 2011