A364263 -id:A364263 - cp's OEIS frontend

A363500 Numbers k between twin primes p, q where k+p and k+q are also twin primes, and kp and kq 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

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

nonn

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

Subsequence of A066388.

Cf. A364263.

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

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

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cp's OEIS Frontend

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.

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