A239788 Numbers n such that 3n^3 +/- 1 are twin primes.

4, 10, 14, 36, 54, 64, 70, 86, 150, 174, 176, 180, 200, 306, 384, 440, 494, 650, 706, 800, 824, 924, 976, 980, 986, 1020, 1026, 1054, 1360, 1464, 1504, 1506, 1536, 1564, 1604, 1680, 1724, 1736, 2066, 2076, 2116, 2134, 2136, 2166, 2200, 2220, 2314, 2380, 2456

Offset: 1

Author

Derek Orr, Mar 26 2014

Keywords

• nonn
• easy

Comments

Numbers in this sequence are all even.

Examples

			3*4^3-1 = 191 is prime and 3*4^3+1 = 193 is prime. Thus, 4 is a member of this sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A116954, A239787.

Programs

Magma

[n: n in [0..5000] | IsPrime(3*n^3-1) and IsPrime(3*n^3+1)]; // Vincenzo Librandi, Mar 29 2014

Mathematica

Select[Range[5000], PrimeQ[3 #^3 - 1] && PrimeQ[3 #^3 + 1]&] (* Vincenzo Librandi, Mar 29 2014 *)

PARI

s=[]; for(n=1, 3000, if(isprime(3*n^3-1) && isprime(3*n^3+1), s=concat(s, n))); s \\ Colin Barker, Mar 27 2014

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(3*(n**3)+1) and isprime(3*(n**3)-1)}