cp's OEIS Frontend

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.

User: Bryce Case, Jr.

Bryce Case, Jr.'s wiki page.

Bryce Case, Jr. has authored 2 sequences.

A364263 Numbers j such that k=210*j, 2*k, k^2+k, k^2-k all are averages of twin primes.

Original entry on oeis.org

521457, 7235406, 107647749, 123718516, 161881498, 200141522, 215640361, 269177896, 301917955, 352021648, 393455227, 580398355, 716403116, 916268861, 1000979331, 1231997208, 1289093896, 1354550305, 1471667483, 1478187348, 1485031638, 1520586133
Offset: 1

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Author

Bryce Case, Jr. and Antonio Gimenez, Jul 16 2023

Keywords

Comments

A derivative sequence stemming from editorial discussion with Hugo Pfoertner, consisting of GCD-reduced elements of A363500, all of which were determined to be multiples of 210 aside from the first term.

Links

Crossrefs

Cf. A363500.

Programs

  • Go
    // See link.

Formula

a(n) = A363500(n+1)/210. - Jason Yuen, Jun 04 2024

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.

Original entry on oeis.org

6, 109505970, 1519435260, 22606027290, 25980888360, 33995114580, 42029719620, 45284475810, 56527358160, 63402770550, 73924546080, 82625597670, 121883654550, 150444654360, 192416460810, 210205659510, 258719413680, 270709718160, 284455564050, 309050171430
Offset: 1

Views

Author

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

Keywords

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

Crossrefs

Subsequence of A066388.
Cf. A364263.

Programs

  • Go
    // See link.

Formula

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

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