

A123998


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


14



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



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



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



