A123998 - OEIS

A123998

Numbers k such that 2k+1 and 4k+1 are primes.

1, 3, 9, 15, 18, 39, 48, 69, 78, 99, 105, 114, 135, 153, 165, 168, 183, 189, 219, 249, 273, 288, 300, 303, 309, 330, 345, 363, 405, 414, 438, 468, 483, 498, 504, 534, 585, 618, 639, 648, 699, 714, 729, 765, 804, 813, 828, 879, 933, 1005, 1014, 1044, 1065, 1068

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OFFSET

1,2

COMMENTS

Note that if n == 1 (mod 3) then 2n+1 is not prime (except n=1); and if n == 2 (mod 3) then 4n+1 is not prime. Therefore n must be a multiple of 3, except for n=1. - Max Alekseyev, Nov 02 2006

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

J. O'Rourke, Why are this operator's primes the Sophie Germain primes?

MATHEMATICA

Select[Range[1100], And @@ PrimeQ /@ ({2, 4}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

PROG

(Magma) [n: n in [0..1100] |IsPrime(2*n+1) and IsPrime(4*n+1)]; // Vincenzo Librandi, Apr 17 2013

(PARI) is(k) = isprime(2*k+1) && isprime(4*k+1); \\ Jinyuan Wang, Aug 04 2019

CROSSREFS

Cf. A005097, A005098, A124408, A124409, A124410, A124411, A071576.

Sequence in context: A298014 A071347 A093414 * A117105 A261190 A282031

Adjacent sequences: A123995 A123996 A123997 * A123999 A124000 A124001