

A162338


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


1



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
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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.


LINKS



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).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



