A123998 - OEIS

%I #22 Sep 08 2022 08:45:28

%S 1,3,9,15,18,39,48,69,78,99,105,114,135,153,165,168,183,189,219,249,

%T 273,288,300,303,309,330,345,363,405,414,438,468,483,498,504,534,585,

%U 618,639,648,699,714,729,765,804,813,828,879,933,1005,1014,1044,1065,1068

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

%C 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

%H Vincenzo Librandi, <a href="/A123998/b123998.txt">Table of n, a(n) for n = 1..1000</a>

%H J. O'Rourke, <a href="http://mathoverflow.net/questions/48638/">Why are this operator's primes the Sophie Germain primes?</a>

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

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

%o (PARI) is(k) = isprime(2*k+1) && isprime(4*k+1); \\ _Jinyuan Wang_, Aug 04 2019

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

%K nonn,easy

%O 1,2

%A _Artur Jasinski_, Oct 31 2006

%E Extended by _Ray Chandler_, Nov 20 2006