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A201074 Initial primes in prime 5-tuples (p, p+2, p+6, p+8, p+12) preceding the maximal gaps in A201073.

%I A201074 #24 Feb 16 2025 08:33:16
%S A201074 5,11,101,1481,22271,55331,536441,661091,1461401,1615841,5527001,
%T A201074 11086841,35240321,53266391,72610121,92202821,117458981,196091171,
%U A201074 636118781,975348161,1156096301,1277816921,1347962381,2195593481,3128295551
%N A201074 Initial primes in prime 5-tuples (p, p+2, p+6, p+8, p+12) preceding the maximal gaps in A201073.
%C A201074 Prime quintuplets (p, p+2, p+6, p+8, 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 A201073; see more comments there.
%H A201074 Alexei Kourbatov, <a href="/A201074/b201074.txt">Table of n, a(n) for n = 1..64</a>
%H A201074 Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>
%H A201074 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 A201074 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 A201074 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 A201074 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>
%e A201074 The initial four gaps of 6, 90, 1380, 14580 (starting at p=5, 11, 101, 1481) form an increasing sequence of records. Therefore a(1)=5, a(2)=11, a(3)=101, and a(4)=1481. The next gap is smaller, so a new term is not added.
%Y A201074 Cf. A022006 (prime 5-tuples p, p+2, p+6, p+8, p+12), A201073, A233432.
%K A201074 nonn
%O A201074 1,1
%A A201074 _Alexei Kourbatov_, Nov 26 2011