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A003306 Numbers k such that 2*3^k + 1 is prime.
(Formerly M0951)
20
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, 6236772, 10852677 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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.
MATHEMATICA
lst={}; Do[If[PrimeQ[2*3^n+1], AppendTo[lst, n]], {n, 0, 10^4}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)
PROG
(PARI) is(n)=isprime(2*3^n+1) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
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 Paul S. Vanderveen, Feb 09 2020
a(46) found by Ryan Propper, Feb 14 2020
a(47)-a(48) found by Ryan Propper added by Paul S. Vanderveen, Jan 08 2023
STATUS
approved

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Last modified February 27 19:52 EST 2024. Contains 370378 sequences. (Running on oeis4.)