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.

Showing 1-2 of 2 results.

A174920 List of primes p1 such that (p1,p2) are twin primes where both 2*p1+p2 and p1+2*p2 are primes.

Original entry on oeis.org

3, 5, 59, 269, 1949, 2999, 6359, 11489, 11549, 14549, 18539, 19889, 21839, 31079, 32909, 32969, 33329, 33599, 42569, 42839, 50459, 53549, 58109, 68879, 70199, 74609, 79229, 80909, 93809, 96329, 98909, 104309, 109139, 114599, 121019, 125789
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 02 2010

Keywords

Comments

Terms >5 are congruent to 29 mod 30. - Zak Seidov, May 10 2012
Also 2*p1+p2 and p1+2*p2 are twin primes. - Zak Seidov, May 10 2012

Examples

			a(1)=3 because 3, 5 are twin primes and 2*3+5=11, 3+2*5=13 are also primes.

Links

Crossrefs

Cf. A001359, A174913, A174915, A174916, A174917, A177335.
Cf. A132929, A177336.

Programs

  • Magma
    [NthPrime(n): n in [1..12000] | forall{p: p in [NthPrime(n)+2,3*NthPrime(n)+2,3*NthPrime(n)+4] | IsPrime(p)}]; // Bruno Berselli, May 10 2012
  • Maple
    select(q -> isprime(q) and isprime(q+2) and isprime(3*q+2) and isprime(3*q+4), [3,5,seq(i,i=29..200000,30)]); # Robert Israel, May 06 2019
  • Mathematica
    lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[2*p1+p2]&&PrimeQ[p1+2*p2],AppendTo[lst,p1]],{n,8!}];lst

Formula

From Wesley Ivan Hurt, May 03 2022: (Start)
a(n) = A132929(n) - 1.
a(n) = A177336(n) - 2. (End)

A177336 Greater of twin primes p such that 3*p-2 is also greater of twin primes.

Original entry on oeis.org

5, 7, 61, 271, 1951, 3001, 6361, 11491, 11551, 14551, 18541, 19891, 21841, 31081, 32911, 32971, 33331, 33601, 42571, 42841, 50461, 53551, 58111, 68881, 70201, 74611, 79231, 80911, 93811, 96331, 98911, 104311, 109141, 114601, 121021, 125791
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 07 2010

Keywords

Examples

			a(1) = 5 because 5 is the greater of the twin primes (3, 5) and 3*5 - 2 = 13 is the greater of the twin primes (11, 13).

Links

Crossrefs

Cf. A006512, A038869, A088878.
Cf. A132929, A174920.

Programs

  • Magma
    [p:p in PrimesInInterval(3,130000)| IsPrime(p-2) and IsPrime(3*p-2) and IsPrime(3*p-4)]; // Marius A. Burtea, Dec 23 2019
  • Mathematica
    Select[Range[3, 126000], And @@ PrimeQ[{#, # - 2, 3# - 2, 3# - 4}] &] (* Amiram Eldar, Dec 23 2019 *)

Formula

From Wesley Ivan Hurt, May 03 2022: (Start)
a(n) = A132929(n) + 1.
a(n) = A174920(n) + 2. (End)

Extensions

Definition corrected, 1231 and 1483 inserted, and all values above 3000 corrected by R. J. Mathar, May 10 2010
Terms corrected to match definition by D. S. McNeil, May 10 2010
Name corrected by Amiram Eldar, Dec 23 2019
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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