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%I M0803 #73 Jun 03 2020 16:50:49
%S 0,1,2,3,6,14,15,39,201,249,885,1005,1254,1635,3306,3522,9602,19785,
%T 72698,233583,328689,537918,887535,980925,1154598,1499606,1936890,
%U 2016951,2143374
%N Numbers n such that 4*3^n + 1 is prime.
%C a(27) > 1.5*10^6. - _Matthias Baur_, Jan 16 2020
%C a(20) > 2*10^5. - _Robert Price_, Nov 23 2013
%C Primes resulting from a(1)-a(19) are confirmed primes (not probable primes) using BLS (N-1/N+1) test in pfgw. - _Robert Price_, Nov 23 2013
%C From _Matthias Baur_, Jan 16 2020: (Start)
%C Double checked to n=2*10^5, tested further to n=1.5*10^6 using the sieve programs newpgen and srsieve and using Jean Penné's LLR application (BLS (N-1/N+1) test).
%C a(20) was already known in 2005, but was not listed here until 2018 (see Prime Pages link). (End)
%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="https://www.utm.edu/research/primes/">The Prime Pages</a>
%H Douglas E. Iannucci, Deng Moujie and Graeme L. Cohen, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cohen2/cohen50.html">On Perfect Totient Numbers</a>, J. Integer Sequences, 6 (2003), #03.4.5.
%H P. Loomis, M. Plytage and J. Polhill, <a href="http://www.jstor.org/stable/27646564">Summing up the Euler 'phi' function</a>, The College Mathematics Journal, vol. 39 (2008), pp. 34-42.
%H H. C. Williams and C. R. Zarnke, <a href="http://www.jstor.org/stable/2005886">Some prime numbers of the forms 2*3^n+1 and 2*3^n-1</a>, Math. Comp., 26 (1972), 995-998.
%t a[n_]:=If[PrimeQ[4*3^n + 1 ], n]; DeleteCases[Array[a, 40, 0], Null] (* _Stefano Spezia_, Nov 12 2018 *)
%o (PARI) a(n) = isprime(4*3^n + 1) \\ _Michel Marcus_, Jul 12 2013
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_, _Chris K. Caldwell_
%E a(15)-a(17) from Douglas Burke (dburke(AT)nevada.edu)
%E a(18) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)sanef.com), Jan 26 2004
%E a(19) from _Robert Price_, Nov 23 2013
%E a(20)-a(21) from _Matthias Baur_, Nov 07 2018
%E a(22) from _Matthias Baur_, Dec 06 2018
%E a(23)-a(24) from _Matthias Baur_, Jul 23 2019
%E a(25) from _Matthias Baur_, Dec 07 2019
%E a(26) from _Matthias Baur_, Jan 16 2020
%E a(27)-a(29) from _Ryan Propper_, May 08 2020
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