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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
Sequence in context: A298014 A071347 A093414 * A117105 A261190 A282031
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Oct 31 2006
EXTENSIONS
Extended by Ray Chandler, Nov 20 2006
STATUS
approved

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Last modified June 23 06:39 EDT 2024. Contains 373629 sequences. (Running on oeis4.)