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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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).
Adjacent sequences: A003304 A003305 A003306 this_sequence A003308 A003309 A003310
Sequence in context: A047221 A032967 A111101 this_sequence A105601 A033082 A084406
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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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