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%I #35 Sep 05 2021 02:33:07
%S 3,5,11,29,419,521,1931,6449,10007,28349,107507,173429,569321,913637,
%T 1349531,3593201,18286391,80528741,83528411,591792347,1971409091,
%U 2061246347,8579208791,13861166687,15250041281,27034148369,27066034997,54125499299,315361055237
%N Lesser of lonely twin primes pairs with increasing distance to nearest prime.
%H Dmitry Petukhov, <a href="/A262936/b262936.txt">Table of n, a(n) for n = 1..40</a>
%F a(n) = p(i) if ( (p(i+1) = p(i)+2) AND (min(p(i+2)-p(i+1), p(i)-p(i-1)) > a(n-1)) ), where a(0) = 0, p(k) = prime(k) = A000040(k).
%e (3,5) is a twin primes pair, min(7-5, 3-2)=1, therefore a(1)=3.
%e (5,7) is a twin primes pair, min(11-7, 5-3)=2>1, therefore a(2)=5.
%e (11,13) is a twin primes pair, min(17-13, 11-7)=4>2, therefore a(3)=11.
%o (PARI) {m=0; q=5; s=3; t=2; forprime(p=6, 10^9, if((q-s==2) && (min(p-q, s-t)>m), m=min(p-q, s-t); print1(s, ", ") ); t=s; s=q; q=p;)}
%Y Subsequence of A001359.
%Y Cf. A035789, A262935, A347280.
%K nonn
%O 1,1
%A _Dmitry Petukhov_, Oct 04 2015
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