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Increasing gaps among twin primes: the largest prime of the starting twin pair.
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%I #40 May 13 2022 07:57:23

%S 5,7,19,43,73,313,349,661,2383,5881,13399,18541,24421,62299,187909,

%T 687523,688453,850351,2868961,4869913,9923989,14656519,17382481,

%U 30752233,32822371,96894043,136283431,234966931,248641039,255949951,390817729,698542489,2466641071

%N Increasing gaps among twin primes: the largest prime of the starting twin pair.

%C Has many terms in common with A054691, but neither of the two is a subsequence of the other one. - _M. F. Hasler_, May 07 2022

%H Martin Raab, <a href="/A036061/b036061.txt">Table of n, a(n) for n = 1..82</a>

%H Alexei Kourbatov and Marek Wolf, <a href="https://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/twin_gaps.html">Gaps between twin primes</a>

%H Randall Rathbun, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;b24a8d59.9811">Twin Prime Gaps</a>, NMBRTHRY Mailing List, Nov 23 1998.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>

%F a(n) = A036062(n) - A036063(n).

%F a(n) = A113275(n) + 2.

%t Block[{s = Select[Partition[Prime@ Range[10^7], 2, 1], Subtract @@ # == -2 &][[All, -1]], t}, t = Differences@ s; Map[s[[FirstPosition[t, #]]] &, Union@ FoldList[Max, t]][[All, 1]]] (* _Michael De Vlieger_, Jan 18 2019 *)

%Y Cf. A036062, A036063, A002386, A113275.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E Terms 5, 7 prepended by _Max Alekseyev_, Nov 05 2015

%E a(17) corrected and a(31)-a(33) from _Sean A. Irvine_, Oct 21 2020