A003306 - OEIS

%I M0951 #65 Feb 20 2023 15:18:24

%S 0,1,2,4,5,6,9,16,17,30,54,57,60,65,132,180,320,696,782,822,897,1252,

%T 1454,4217,5480,6225,7842,12096,13782,17720,43956,64822,82780,105106,

%U 152529,165896,191814,529680,1074726,1086112,1175232,1277862,1346542,3123036,3648969,5570081,6236772,10852677

%N Numbers k such that 2*3^k + 1 is prime.

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

%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/">The Prime Pages</a>

%H Hartosh Singh Bal and Gaurav Bhatnagar, <a href="https://arxiv.org/abs/1903.09619">Prime number conjectures from the Shapiro class structure</a>, arXiv:1903.09619 [math.NT], 2019. See also Integers (2020) Vol. 20, <a href="http://math.colgate.edu/~integers/u11/u11.pdf">Article A11.</a>

%H W. Keller and J. Richstein, <a href="https://doi.org/10.1090/S0025-5718-04-01666-7">Solutions of the congruence a^(p-1) == 1 (mod p^r)</a>, Math. Comp. 74 (2005), 927-936.

%H H. C. Williams and C. R. Zarnke, <a href="https://doi.org/10.1090/S0025-5718-1972-0314747-X">Some prime numbers of the forms 2A3^n+1 and 2A3^n-1</a>, Math. Comp., 26 (1972), 995-998.

%t lst={};Do[If[PrimeQ[2*3^n+1], AppendTo[lst, n]], {n, 0, 10^4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 19 2008 *)

%o (PARI) is(n)=isprime(2*3^n+1) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A056802 (k such that 2*9^k + 1 is prime).

%Y Cf. A111974 (primes of the form 2*3^k + 1), A003307 (k such that 2*3^k - 1 is prime).

%K nonn

%O 1,3

%A _N. J. A. Sloane_, _Chris K. Caldwell_

%E More terms from _T. D. Noe_, Aug 24 2005

%E More terms from _David Broadhurst_, Feb 14 2010

%E Another term from _David Broadhurst_, Feb 22 2010

%E a(42)-a(45) found by _Ryan Propper_ and _Paul S. Vanderveen_, Feb 09 2020

%E a(46) found by _Ryan Propper_, Feb 14 2020

%E a(47)-a(48) found by _Ryan Propper_ added by _Paul S. Vanderveen_, Jan 08 2023