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

1,1

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

Links

Table of n, a(n) for n=1..56.

Example

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.

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 *)

Prog

(Magma) [ q: q in PrimesUpTo(800) | IsPrime(3*q+1) or IsPrime(3*q+2) ]; // Klaus Brockhaus, Jul 06 2009
(PARI) isA162338(n) = isprime(n) && (isprime(3*n+1) || isprime(3*n+2)) \\ Michael B. Porter, Jan 30 2010

Crossrefs

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

Sequence in context: A040974 A049557 A042991 * A339342 A052015 A042992

Adjacent sequences: A162335 A162336 A162337 * A162339 A162340 A162341

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 01 2009

Extensions

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

Status

approved