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

Offset: 1

Author

Artur Jasinski, Oct 31 2006

Keywords

• nonn
• easy

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?

Crossrefs

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

Programs

Magma

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

Mathematica

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

PARI

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

Extensions

Extended by Ray Chandler, Nov 20 2006