%I
%S 3,5,17,41,71,311,347,659,2381,5879,13397,18539,24419,62297,187907,
%T 687521,688451,850349,2868959,4869911,9923987,14656517,17382479,
%U 30752231,32822369,96894041,136283429,234966929,248641037,255949949
%N Lesser of twin primes for which the gap before the following twin primes is a record.
%H Max Alekseyev, <a href="/A113275/b113275.txt">Table of n, a(n) for n = 1..75</a>
%H Alexei Kourbatov, <a href="http://arxiv.org/abs/1301.2242">Maximal gaps between prime ktuples: a statistical approach</a>, arXiv preprint arXiv:1301.2242 [math.NT], 2013.
%H Alexei Kourbatov, <a href="http://arxiv.org/abs/1309.4053">Tables of record gaps between prime constellations</a>, arXiv preprint arXiv:1309.4053 [math.NT], 2013.
%H 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 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/twin_gaps.html">Gaps between twin primes</a>
%F a(n) = A036061(n)  2.
%F a(n) = A036062(n)  A113274(n).
%e The smallest twin prime pair is 3, 5, then 5, 7 so a(1) = 3; the following pair is 11, 13 so a(2) = 5 because 11  5 = 6 > 5  3 = 2; the following pair is 17, 19: since 17  11 = 6 = 11  5 nothing happens; the following pair is 29, 31 so a(3)= 17 because 29  17 = 12 > 11  5 = 6.
%t NextLowerTwinPrim[n_] := Block[{k = n + 2}, While[ !PrimeQ[k]  !PrimeQ[k + 2], k++ ]; k]; p = 3; r = 0; t = {3}; Do[q = NextLowerTwinPrim[p]; If[q > r + p, AppendTo[t, p]; r = q  p]; p = q, {n, 10^9}] (* _Robert G. Wilson v_ *)
%Y Record gaps are given in A113274. Cf. A002386.
%K nonn
%O 1,1
%A _Bernardo Boncompagni_, Oct 21 2005
%E a(22)a(30) from _Robert G. Wilson v_, Oct 22 2005
%E Terms up to a(72) are listed in Kourbatov (2013), terms up to a(75) in Oliveira e Silva's website, added by _Max Alekseyev_, Nov 06 2015
