A130800 Numbers k such that both 2k+1 and 3k+1 are primes.

2, 6, 14, 20, 26, 36, 50, 54, 74, 90, 116, 140, 146, 174, 200, 204, 210, 224, 230, 270, 284, 306, 330, 336, 350, 354, 384, 404, 410, 426, 440, 476, 510, 516, 554, 564, 596, 600, 624, 644, 650, 704, 714, 726, 740, 746, 834, 846, 894, 930, 944, 950, 1026, 1040

Offset

1,1

Comments

Also: k such that A033570(k) is semiprime. All terms are congruent to 0 or 2 modulo 6. - M. F. Hasler, Dec 13 2019

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = 2*A255607(n). - M. F. Hasler, Dec 13 2019

Mathematica

Select[Range[1100], AllTrue[{2, 3}#+1, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 17 2016 *)

Prog

(Magma) [n: n in [0..500] | IsPrime(2*n+1) and IsPrime(3*n+1)]; // Vincenzo Librandi, Nov 23 2010
(PARI) select( is_A130800(n)=isprime(2*n+1)&&isprime(3*n+1), [1..1111]) \\ M. F. Hasler, Dec 13 2019

Crossrefs

Intersection of A005097 and A024892. - M. F. Hasler, Dec 13 2019

Cf. A033570; A255584: semiprimes of the form (4*n+1)*(6*n+1).

Sequence in context: A246068 A032643 A067664 * A067262 A107369 A151731

Adjacent sequences: A130797 A130798 A130799 * A130801 A130802 A130803

Keyword

nonn

Author

Max Alekseyev, Jul 18 2007

Extensions

More terms from Vincenzo Librandi, Mar 26 2010

Status

approved