A162338 Primes q such that q = floor(p/3) for some prime p.

2, 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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 01 2009

Keywords

• nonn

Comments

Primes q such that 3*q+1 or 3*q+2 is prime. Agrees with A023208 except for initial term 2.

Essentially the same as A023208. - R. J. Mathar, Jul 05 2009

Examples

			3 is in the sequence since 11 is prime and floor(11/3) = 3; 11 is not in the sequence since 11 = floor(34/3) = floor(35/3) and neither 34 nor 35 is prime.
		

Crossrefs

Cf. A162337. Essentially the same as A023208 (n and 3n+2 are both prime).

Programs

Magma

[ q: q in PrimesUpTo(800) | IsPrime(3*q+1) or IsPrime(3*q+2) ]; // Klaus Brockhaus, Jul 06 2009

Mathematica

lst={};Do[r=Prime[n];If[PrimeQ[p=Floor[r/3]],AppendTo[lst,p]],{n,6!}];lst
Select[Floor[Prime[Range[350]]/3],PrimeQ] (* Harvey P. Dale, Aug 26 2013 *)
Select[Prime[Range[200]],AnyTrue[3#+{1,2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 07 2019 *)

PARI

isA162338(n) = isprime(n) && (isprime(3*n+1) || isprime(3*n+2)) \\ Michael B. Porter, Jan 30 2010

Extensions

Edited and listed terms verified by Klaus Brockhaus, Jul 06 2009