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 A337435 #8 Sep 02 2020 19:25:05 %S A337435 2,5,25,87,325,213,192,758,500,1158,1668,5383,4217,13130,15180,4713, %T A337435 5955,19583,66642,17127,48108,49485,28905,171005,175530,61838,314192, %U A337435 76967,192637,96147,812768,708780,139725,295862,354545,1572328,1240860,1681368,773453,1300602 %N A337435 6*a(n) - 1 is the least prime p of a pair of twin primes p, p + 2, for which the prime gap immediately below p achieves the size 2*A007494(n). %C A337435 Apart from the atypical case [3, 5, 7], prime gaps p - prevprime(p-1) preceding a pair of twin primes p, p+2 can only have the sizes 4, 6, 10, 12, 16, 18, ..., i.e., numbers k of the form 2*(k == 0 or 2 mod 3) = 2*A007494(n). %e A337435 a(1) = 2: The first occurrence of 3 consecutive primes [p-4, p, p+2] is at p = 6*a(1) - 1 = 11 -> [7, 11, 13], %e A337435 a(2) = 5: consecutive primes [p-6, p, p+2] first occur at p = 6*a(2) - 1 = 29 -> [23, 29, 31], %e A337435 a(3) = 25: consecutive primes [p-10, p, p+2] first occur at p = 6*a(3) - 1 = 149 -> [139, 149, 151]. %Y A337435 Cf. A007494, A329158, A329159, A337436. %K A337435 nonn %O A337435 1,1 %A A337435 _Hugo Pfoertner_, Sep 02 2020