A157834 Numbers n such that 3n-2 and 3n+2 are both prime.

3, 5, 7, 13, 15, 23, 27, 33, 35, 37, 43, 55, 65, 75, 77, 93, 103, 105, 117, 127, 133, 147, 153, 155, 163, 167, 205, 215, 225, 247, 253, 257, 275, 285, 287, 293, 295, 303, 313, 323, 337, 363, 365, 405, 427, 433, 435, 475, 477, 483, 495, 497, 517

Offset: 1

Author

Kyle D. Balliet, Mar 07 2009

Keywords

• nonn

Comments

Barycenter of cousin primes (A029708; see also A029710, A023200, A046132), divided by 3. When p>3 and p+4 both are prime, then p = 1 (mod 6) and p+2 = 3 (mod 6). - M. F. Hasler, Jan 14 2013

Examples

			15*3 +/- 2 = 43,47 (both prime).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A024893 and A153183.

Programs

Magma

[n: n in [1..1000]|IsPrime(3*n-2)and IsPrime(3*n+2)] // Vincenzo Librandi, Dec 13 2010

Maple

select(t -> isprime(3*t+2) and isprime(3*t-2), [seq(t,t=3..1000,2)]); # Robert Israel, May 28 2017

Mathematica

Select[Range[600],AllTrue[3#+{2,-2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 03 2019 *)

Formula

Intersection of A024893 and A153183.

a(n) = A029708(n)/3. - Zak Seidov, Aug 07 2009

a(n) = A056956(n)*2+1 = (A029710(n)+2)/3 = (A023200(n+1)+2)/3. - M. F. Hasler, Jan 14 2013