

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
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OFFSET

1,3


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

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^(p1) == 1 (mod p^r), Math. Comp. 74 (2005), 927936.
H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2A3^n+1 and 2A3^n1, Math. Comp., 26 (1972), 995998.


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
Adjacent sequences: A003303 A003304 A003305 * A003307 A003308 A003309


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Chris K. Caldwell


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 added by Paul S. Vanderveen, Feb 09 2020
a(46) found by Ryan Propper, Feb 14 2020


STATUS

approved



