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

Author

Max Alekseyev, Jul 18 2007

Keywords

• nonn

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

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).

Programs

Magma

[n: n in [0..500] | IsPrime(2*n+1) and IsPrime(3*n+1)]; // Vincenzo Librandi, Nov 23 2010

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 *)

PARI

select( is_A130800(n)=isprime(2*n+1)&&isprime(3*n+1), [1..1111]) \\ M. F. Hasler, Dec 13 2019

Formula

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

Extensions

More terms from Vincenzo Librandi, Mar 26 2010