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 A003307 Numbers k such that 2*3^k - 1 is prime. (Formerly M0823) 31

%I M0823

%S 1,2,3,7,8,12,20,23,27,35,56,62,68,131,222,384,387,579,644,1772,3751,

%T 5270,6335,8544,9204,12312,18806,21114,49340,75551,90012,128295,

%U 143552,147488,1010743,1063844,1360104

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

%D R. K. Guy, Unsolved Problems in Theory of Numbers, Section A3.

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

%H Kevin A. Broughan and Qizhi Zhou, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Broughan/bro32.html">On the Ratio of the Sum of Divisors and Euler's Totient Function II</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.

%H Steven Harvey, <a href="http://harvey563.tripod.com/wills.txt">Williams Primes</a>

%H W. Keller, J. Richstein, <a href="http://dx.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, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa39/aa3912.pdf">The primality of certain integers of the form 2Ar^n - 1</a>, Acta Arith. 39 (1981), 7-17.

%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 2*3^n+1 and 2*3^n-1</a>, Math. Comp., 26 (1972), 995-998.

%o (PARI) for(n=1,1e4,if(ispseudoprime(2*3^n-1),print1(n", "))) \\ _Charles R Greathouse IV_, Jul 16 2011

%Y Cf. A002235, A046865, A079906, A046866, A001771, A005541, A056725, A046867, A079907.

%Y Cf. A079363 (primes of the form 2*3^n-1), A003306 (n such that 2*3^n+1 is prime).

%K nonn,hard,nice

%O 1,2

%A _N. J. A. Sloane_

%E More terms from Douglas Burke (dburke(AT)nevada.edu)

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

%E Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

%E a(35) from _Borys Jaworski_, Sep 02 2011

%E a(36) from _Borys Jaworski_, Feb 13 2012

%E a(37) from _Jeppe Stig Nielsen_, Sep 28 2018

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)