1,1

Larger twin primes are found on either side of 6x, so my highly-unoptimized code simply keeps adding 6 and performing the requisite primality checks using golang's "ProbablyPrime" function, a combination of Miller-Rabin and Baillie-PSW, accurate up to 2^64. Based on seminal work by fellow OEIS contributor Antonio Gimenez.

To generate, k = 6x.

p = k-1, q = k+1, check the primality of k+p, k+q, then check the primality of ((k*p) +/- 1) and ((k*q) +/- 1).

If k > x+1 and x > 1, then all eight primes are not divisible by x. If k > 8, then k == 0 (mod 210). - Jason Yuen, Jun 02 2024

Jason Yuen, Table of n, a(n) for n = 1..10000 (first 49 terms from Bryce Case, Jr.)

Bryce Case, Jr., a363500.go

a(n) = 210*A364263(n-1) for n > 1. - Hugo Pfoertner, Jun 03 2024

(Go) // See link.

Subsequence of A066388.

Cf. A364263.

Sequence in context: A182792 A067484 A337083 * A193150 A307896 A182793

Adjacent sequences: A363497 A363498 A363499 * A363501 A363502 A363503

Bryce Case, Jr. and Antonio Gimenez, Jun 05 2023

approved