A023208 Primes p such that 3*p + 2 is also prime.

3, 5, 7, 13, 17, 19, 23, 29, 37, 43, 59, 79, 83, 89, 97, 103, 127, 139, 149, 163, 167, 173, 197, 199, 227, 233, 239, 257, 269, 293, 313, 317, 337, 349, 353, 367, 383, 397, 409, 419, 433, 439, 457, 479, 499, 503, 523, 569, 577, 607, 643, 659, 709, 757, 769, 797, 859, 863

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

Also, son primes of order 1. For smallest son primes of order n see A136027 (also definition). For son primes of order 2 see A136082. - Artur Jasinski, Dec 12 2007

Links

• Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 1000 terms from _Zak Seidov_)
• Rosemary Sullivan and Neil Watling, Independent divisibility pairs on the set of integers from 1 to n, INTEGERS 13 (2013) #A65.

Crossrefs

Cf. A023208, A094524, A136019, A136020, A136026, A136027, A136082, A136083, A136084, A136085, A136086, A136087, A136088, A136089, A136090, A136091.

Programs

Haskell

a023208 n = a023208_list !! (n-1)
a023208_list = filter ((== 1) . a010051 . (+ 2) . (* 3)) a000040_list
-- Reinhard Zumkeller, Aug 15 2011

Magma

[n: n in PrimesUpTo(900) | IsPrime(3*n+2)]; // Vincenzo Librandi, Nov 20 2010

Mathematica

n = 1; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, (Prime[k] - 2n)/(2n + 1)]], {k, 1, 1000}]; a (* Artur Jasinski, Dec 12 2007 *)

PARI

isA023208(n) = isprime(n) && isprime(3*n+2) \\ Michael B. Porter, Jan 30 2010

Extensions

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar