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A123998
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Numbers n such that 2n+1 and 4n+1 are primes.
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12
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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; internal format)
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OFFSET
| 1,2
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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
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LINKS
| J. O'Rourke, Why are this operator's primes the Sophie Germain primes?
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MATHEMATICA
| Select[Range[1100], And @@ PrimeQ /@ ({2, 4}*# + 1) &] (*Chandler*)
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CROSSREFS
| Cf. A005097, A005098, A124408-A124411, A071576.
Sequence in context: A071123 A071347 A093414 * A117105 A162488 A194041
Adjacent sequences: A123995 A123996 A123997 * A123999 A124000 A124001
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Oct 31 2006
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 20 2006
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