A165682 Primes p such that 3*p*(p-1)+1 is also prime.

2, 3, 5, 7, 11, 29, 31, 43, 53, 59, 67, 89, 109, 137, 157, 173, 197, 239, 313, 347, 353, 389, 449, 521, 547, 557, 571, 577, 599, 613, 647, 677, 733, 743, 787, 857, 907, 941, 977, 1051, 1069, 1093, 1153, 1193, 1223, 1229, 1237, 1303, 1433, 1453, 1459, 1481, 1571

Offset

1,1

Links

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

Formula

3*a(n)*(a(n)-1)+1 = A165683(n).

Example

For p=5 = a(3), 3*p^2-3*p+1=61 = A165683(3). For a(4)=p=7: 3*p^2-3*p+1=127 = A165684(4).

Mathematica

Select[Prime[Range[800]], PrimeQ[3 # (# - 1) + 1]&] (* Vincenzo Librandi, Apr 15 2013 *)

Prog

(Magma) [p: p in PrimesUpTo(1600) | IsPrime(3*p*(p-1)+1)]; // Vincenzo Librandi, Apr 15 2013

Crossrefs

Cf. A165681, A165683.

Sequence in context: A036342 A114421 A167119 * A296924 A343423 A175711

Adjacent sequences: A165679 A165680 A165681 * A165683 A165684 A165685

Keyword

nonn,easy

Author

Vincenzo Librandi, Sep 24 2009

Extensions

2 and 3 inserted by R. J. Mathar, Sep 26 2009

Status

approved