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A003307
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Numbers n such that 2*3^n - 1 is prime.
(Formerly M0823)
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21
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1, 2, 3, 7, 8, 12, 20, 23, 27, 35, 56, 62, 68, 131, 222, 384, 387, 579, 644, 1772, 3751, 5270, 6335, 8544, 9204, 12312, 18806, 21114, 49340, 75551, 90012, 128295, 143552, 147488, 1010743
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| R. K. Guy, Unsolved Problems in Theory of Numbers, Section A3.
Wilfrid Keller and Jorg Richstein, Solutions of the congruence a^(p-1) = 1 (mod p^r), Math. Comp., Vol. 74 (2005), 927-936.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. C. Williams, The primality of certain integers of the form 2Ar^n - 1, Acta Arith. 39 (1981), 7-17.
H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2*3^n+1 and 2*3^n-1, Math. Comp., 26 (1972), 995-998.
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LINKS
| Steven Harvey, Williams Primes
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MATHEMATICA
| lst={}; Do[p=2*3^n-1; If[PrimeQ[p], AppendTo[lst, n]], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 05 2008]
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PROG
| (PARI) for(n=1, 1e4, if(ispseudoprime(2*3^n-1), print1(n", "))) \\ Charles R Greathouse IV, Jul 16, 2011
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CROSSREFS
| Cf. A002235, A046865, A079906, A046866, A001771, A005541, A056725, A046867, A079907.
Cf. A079363 (primes of the form 2*3^n-1), A003306 (n such that 2*3^n+1 is prime).
Sequence in context: A111101 A184860 A145489 * A105601 A199971 A033082
Adjacent sequences: A003304 A003305 A003306 * A003308 A003309 A003310
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KEYWORD
| nonn,hard,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Douglas Burke (dburke(AT)nevada.edu)
More terms from T. D. Noe (noe(AT)sspectra.com), Aug 24 2005
Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
One more term from Borys Jaworski (borris_j(AT)poczta.onet.pl), Sep 02 2011
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