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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.
2
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
KEYWORD
nonn
AUTHOR
STATUS
approved