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%I #7 Nov 08 2019 18:17:55
%S 1,2,5,25,87,192,500,1158,1668,4217,4713,5955,17127,28905,61838,76967,
%T 96147,139725,260342,1061923,1205080,4663498,8871842,11732765,
%U 32534740,42313103,77638122,92523718,282054523,728833340,2940948542,3344803093,11810906035
%N Let P1>=3, P2, P3 be consecutive primes, with P3-P2=2. a(n)=(P2+P3)/12 when P2-P1 sets a record.
%C 6*a(n)-1, 6*a(n)+1 are twin primes such that the prime gap immediately preceding 6*a(n)-1 sets a record. The corresponding gap lengths are provided in A329159.
%o (PARI) p1=3;p2=5;r=0;forprime(p3=7,1e9,if(p3-p2==2,d=p2-p1;if(d>r,r=d;print1((p2+p3)/12,", ")));p1=p2;p2=p3)
%Y Cf. A002822, A084105, A329159, A329160, A329161, A329164, A329165.
%K nonn
%O 1,2
%A _Hugo Pfoertner_, Nov 06 2019
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