This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329160 #5 Nov 08 2019 18:18:08 %S A329160 1,5,23,33,87,278,495,1293,2027,2690,4245,6773,13283,24938,28893, %T A329160 44270,67475,139708,224922,315893,971000,1723960,3319792,6228255, %U A329160 7013717,13194622,25321985,31864375,32163975,65155398,86090027,381175405,452803425 %N A329160 Let P1>=5, P2, P3 be consecutive primes, with P2-P1=2. a(n)=(P1+P2)/12 when P3-P2 sets a record. %C A329160 6*a(n)-1, 6*a(n)+1 are twin primes such that the prime gap immediately following 6*a(n)+1 sets a record. The corresponding gap lengths are provided in A329161. %e A329160 See A329161. %o A329160 (PARI) p1=5; p2=7; r=0; forprime(p3=11, 1e9, if(p2-p1==2, d=p3-p2; if(d>r, r=d; print1((p1+p2)/12, ", "))); p1=p2; p2=p3) %Y A329160 Cf. A002822, A084105, A329158, A329159, A329161, A329164, A329165. %K A329160 nonn %O A329160 1,2 %A A329160 _Hugo Pfoertner_, Nov 08 2019