A104163 Primes p such that (2p+1)/3 is prime.

7, 19, 43, 61, 79, 109, 151, 163, 223, 271, 349, 421, 439, 523, 601, 613, 631, 673, 691, 811, 853, 919, 991, 1009, 1051, 1063, 1153, 1213, 1231, 1279, 1321, 1429, 1531, 1549, 1663, 1693, 1789, 1801, 1873, 1933, 1951, 2113, 2143, 2179, 2221, 2239, 2503, 2539

Offset: 1

Author

Roger L. Bagula, Mar 10 2005

Keywords

• nonn
• easy

Comments

Dickson's conjecture implies that this sequence is infinite. - Charles R Greathouse IV, Jul 31 2012

Examples

			7 is in the sequence because (2 * 7 + 1)/3 = 5, which is also prime.
19 is in the sequence because (2 * 19 + 1)/3 = 13, which is also prime.
		

Links

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

Crossrefs

Cf. A005384.

Programs

Mathematica

Select[Range[7, 2539, 2], PrimeQ[#] && PrimeQ[(2# + 1)/3]&] (* Zak Seidov, Jul 31 2012 *)
Select[Prime[Range[400]], PrimeQ[(2 # + 1) / 3]&] (* Vincenzo Librandi, Apr 14 2013 *)

PARI

is(n)=n%3==1 && isprime((2*n+1)/3) && isprime(n) \\ Charles R Greathouse IV, Jul 31 2012

Formula

a(n)=(3*A158708(n+1)-1)/2 Zak Seidov, Jul 31 2012

Extensions

New name from Charles R Greathouse IV, Jul 31 2012