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%I M2420 #64 Mar 22 2024 12:22:03
%S 3,5,7,13,23,43,281,359,487,577,1579,1663,1741,3191,9209,11257,12743,
%T 13093,17027,26633,104243,134227,152287,700897,1205459,1896463,
%U 2533963,2674381
%N Numbers k such that (3^k + 1)/4 is prime.
%C Prime repunits in base -3.
%D J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%H J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H H. Dubner, <a href="/A028491/a028491.pdf">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
%H H. Dubner and T. Granlund, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.
%H H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H S. S. Wagstaff, Jr., <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H R. G. Wilson, v, <a href="/A084740/a084740.pdf">Letter to N. J. A. Sloane, circa 1991.</a>
%t lst={};Do[If[PrimeQ[(3^n+1)/4], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)
%o (PARI) is(n)=ispseudoprime((3^n+1)/4) \\ _Charles R Greathouse IV_, Apr 29 2015
%K hard,nonn,more
%O 1,1
%A _N. J. A. Sloane_, _Robert G. Wilson v_
%E a(20) from _Robert G. Wilson v_, Apr 11 2005
%E a(22)=134227 corresponds to a probable prime discovered by _Paul Bourdelais_, Nov 08 2007
%E a(23)=152287 corresponds to a probable prime discovered by _Paul Bourdelais_, Apr 07 2008
%E a(24)=700897 corresponds to a probable prime discovered by _Paul Bourdelais_, Apr 05 2010
%E a(25)=1205459 corresponds to a probable prime discovered by _Paul Bourdelais_, Aug 28 2015
%E a(26)=1896463 corresponds to a probable prime discovered by _Paul Bourdelais_, Jan 30 2020
%E a(27)=2533963 corresponds to a probable prime discovered by _Paul Bourdelais_, Mar 06 2020
%E a(28) from _Paul Bourdelais_, Mar 22 2024
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