A241120 Primes p such that (p^3 + 2)/3 is prime.

13, 19, 31, 193, 211, 223, 229, 271, 331, 571, 619, 691, 739, 751, 853, 991, 1009, 1039, 1051, 1231, 1303, 1321, 1549, 1741, 1789, 1831, 1993, 1999, 2029, 2089, 2113, 2143, 2203, 2311, 2521, 2551, 2683, 2749, 2851, 3121, 3259, 3331, 3571, 3631, 3823, 3853, 4093

Offset: 1

Author

K. D. Bajpai, Apr 16 2014

Keywords

• nonn

Examples

			13 is prime and appears in the sequence because (13^3 + 2)/3 = 733 which is a prime.
31 is prime and appears in the sequence because (31^3 + 2)/3 = 9931 which is a prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..8879

Crossrefs

Cf. A109953 (primes p: (p^2+1)/3 is prime).

Cf. A118915 (primes p: (p^2+5)/6 is prime).

Cf. A118918 (primes p: (p^2+11)/12 is prime).

Cf. A241101 (primes p: (p^3-4)/3 is prime).

Programs

Maple

KD:= proc() local a,b;a:=ithprime(n); b:=(a^3+2)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);

Mathematica

Select[Prime[Range[500]], PrimeQ[(#^3 + 2)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 2)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}]          (* b-file *)

PARI

s=[]; forprime(p=2, 8000, if((p^3+2)%3==0 && isprime((p^3+2)/3), s=concat(s, p))); s \\ Colin Barker, Apr 16 2014