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A003306
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Numbers k such that 2*3^k + 1 is prime.
(Formerly M0951)
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20
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0, 1, 2, 4, 5, 6, 9, 16, 17, 30, 54, 57, 60, 65, 132, 180, 320, 696, 782, 822, 897, 1252, 1454, 4217, 5480, 6225, 7842, 12096, 13782, 17720, 43956, 64822, 82780, 105106, 152529, 165896, 191814, 529680, 1074726, 1086112, 1175232, 1277862, 1346542, 3123036, 3648969, 5570081
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OFFSET
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1,3
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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).
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LINKS
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Table of n, a(n) for n=1..46.
C. K. Caldwell, The Prime Pages
Hartosh Singh Bal and Gaurav Bhatnagar, Prime number conjectures from the Shapiro class structure, arXiv:1903.09619 [math.NT], 2019. See also Integers (2020) Vol. 20, Article A11.
W. Keller and J. Richstein, Solutions of the congruence a^(p-1) == 1 (mod p^r), Math. Comp. 74 (2005), 927-936.
H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2A3^n+1 and 2A3^n-1, Math. Comp., 26 (1972), 995-998.
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MATHEMATICA
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lst={}; Do[If[PrimeQ[2*3^n+1], AppendTo[lst, n]], {n, 0, 10^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)
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PROG
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(PARI) is(n)=isprime(2*3^n+1) \\ Charles R Greathouse IV, Feb 17 2017
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CROSSREFS
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Cf. A056802 (k such that 2*9^k + 1 is prime).
Cf. A111974 (primes of the form 2*3^k + 1), A003307 (k such that 2*3^k - 1 is prime).
Sequence in context: A056635 A288429 A163116 * A250305 A136585 A122721
Adjacent sequences: A003303 A003304 A003305 * A003307 A003308 A003309
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Chris K. Caldwell
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EXTENSIONS
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More terms from T. D. Noe, Aug 24 2005
More terms from David Broadhurst, Feb 14 2010
Another term from David Broadhurst, Feb 22 2010
a(42)-a(45) found by Ryan Propper and added by Paul S. Vanderveen, Feb 09 2020
a(46) found by Ryan Propper, Feb 14 2020
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STATUS
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approved
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