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

1,1

Comments

Numbers in this sequence are all even.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A116954, A239787.

Sequence in context: A125302 A365679 A175588 * A136862 A191635 A123925

Adjacent sequences: A239785 A239786 A239787 * A239789 A239790 A239791

Keyword

nonn,easy

Author

Derek Orr, Mar 26 2014

Status

approved