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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 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

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