A003306 Numbers k such that 2*3^k + 1 is prime. (Formerly M0951)

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

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..48.

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

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 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