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

1,1

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

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Intersection of A024893 and A153183.

Sequence in context: A007591 A097687 A032911 * A192110 A246026 A188574

Adjacent sequences: A157831 A157832 A157833 * A157835 A157836 A157837

Keyword

nonn

Author

Kyle D. Balliet, Mar 07 2009

Status

approved