A241101 Primes p such that (p^3 - 4)/3 is prime.

7, 31, 37, 43, 61, 73, 97, 103, 157, 163, 211, 277, 331, 337, 457, 487, 613, 661, 733, 751, 811, 883, 991, 1021, 1093, 1297, 1321, 1483, 1693, 1741, 1873, 2083, 2113, 2143, 2203, 2221, 2287, 2347, 2437, 2473, 2707, 2917, 3001, 3067, 3187, 3307, 3331, 3343, 3541

Offset: 1

Author

K. D. Bajpai, Apr 16 2014

Keywords

• nonn

Examples

			7 is prime and appears in the sequence because (7^3 - 4)/3 = 113 which is a prime.
31 is prime and appears in the sequence because (31^3 - 4)/3 = 9929 which is a prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..8906

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).

Programs

Maple

KD:= proc() local a,b;a:=ithprime(n); b:=(a^3-4)/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 - 4)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 - 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)

PARI

s=[]; forprime(p=2, 4000, if((p^3-4)%3==0 && isprime((p^3-4)/3), s=concat(s, p))); s \\ Colin Barker, Apr 16 2014