A363500 Numbers k between twin primes p, q where k+p and k+q are also twin primes, and k*p and k*q are between twin primes.

6, 109505970, 1519435260, 22606027290, 25980888360, 33995114580, 42029719620, 45284475810, 56527358160, 63402770550, 73924546080, 82625597670, 121883654550, 150444654360, 192416460810, 210205659510, 258719413680, 270709718160, 284455564050, 309050171430

Offset

1,1

Comments

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

Links

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

Bryce Case, Jr., a363500.go

Formula

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

Prog

(Go) // See link.

Crossrefs

Subsequence of A066388.

Cf. A364263.

Sequence in context: A182792 A067484 A337083 * A193150 A307896 A182793

Adjacent sequences: A363497 A363498 A363499 * A363501 A363502 A363503

Keyword

nonn

Author

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

Status

approved