|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
|