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A201063 Initial primes in prime 5-tuples (p, p+4, p+6, p+10, p+12) preceding the maximal gaps in A201062.

%I A201063 #25 Feb 16 2025 08:33:16
%S A201063 7,97,3457,5647,19417,43777,101107,1621717,3690517,5425747,8799607,
%T A201063 9511417,16388917,22678417,31875577,37162117,64210117,119732017,
%U A201063 200271517,203169007,241307107,342235627,367358347,378200227
%N A201063 Initial primes in prime 5-tuples (p, p+4, p+6, p+10, p+12) preceding the maximal gaps in A201062.
%C A201063 Prime quintuplets (p, p+4, p+6, p+10, p+12) are one of the two types of densest permissible constellations of 5 primes. Maximal gaps between quintuplets of this type are listed in A201062; see more comments there.
%H A201063 Alexei Kourbatov, <a href="/A201063/b201063.txt">Table of n, a(n) for n = 1..71</a>
%H A201063 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H A201063 G. H. Hardy and J. E. Littlewood, <a href="https://dx.doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes</a>, Acta Mathematica, Vol. 44, pp. 1-70, 1923.
%H A201063 Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenprimequintuplets.htm">Maximal gaps between prime 5-tuples</a> (graphs/data up to 10^15)
%H A201063 Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
%H A201063 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e A201063 The gap of 90 between quintuplets starting at p=7 and p=97 is the very first gap, so a(1)=7. The gap of 1770 between quintuplets starting at p=97 and p=1867 is a maximal gap - larger than any preceding gap; therefore a(2)=97. The gap after p=1867 is smaller, so a new term is not added.
%Y A201063 Cf. A022007 (prime 5-tuples p, p+4, p+6, p+10, p+12), A201062, A233433.
%K A201063 nonn
%O A201063 1,1
%A A201063 _Alexei Kourbatov_, Nov 26 2011