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A157834 Numbers n such that 3n-2 and 3n+2 are both prime. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 04:58 EDT 2020. Contains 337267 sequences. (Running on oeis4.)