

A123998


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


13



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


KEYWORD

nonn,easy


AUTHOR

Artur Jasinski, Oct 31 2006


EXTENSIONS

Extended by Ray Chandler, Nov 20 2006


STATUS

approved



