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Search: id:A003307
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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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+0
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
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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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
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Steven Harvey, Williams Primes
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MATHEMATICA
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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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CROSSREFS
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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: A047221 A032967 A111101 this_sequence A105601 A033082 A084406
Adjacent sequences: A003304 A003305 A003306 this_sequence A003308 A003309 A003310
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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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
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