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

Author

Vincenzo Librandi, Sep 24 2009

Keywords

• nonn
• easy

Examples

			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).
		

Links

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

Crossrefs

Cf. A165681, A165683.

Programs

Magma

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

Mathematica

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

Formula

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

Extensions

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