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%I #45 Sep 08 2022 08:45:02
%S 3,59,223,547,773,1009,1823,3803,49223,193247,703393,860029
%N Numbers n such that (9^n + 1)/10 is a prime.
%C Repunit primes in base -9. - _Paul Bourdelais_
%H P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>
%t lst={};Do[p=(9^n+1)/10;If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 29 2008 *)
%t Select[Range[4000], PrimeQ[(9^# + 1)/10] &] (* _Vincenzo Librandi_, Aug 03 2015 *)
%o (PFGW v3.3.1 from primeform.net) pfgw -b2 -f10 bNeg9.txt::
%o ABC2 (9^$a+1)/10 // -f{4*$a}
%o a: primes from 3 to 1e6}
%o (Magma) [n: n in [0..800] | IsPrime((9^n + 1) div 10 )]; // _Vincenzo Librandi_, Aug 03 2015
%o (PARI) first(m)=my(v=vector(m));t=0;for(i=1,m,while(!isprime((9^t + 1)\10),t++);v[i]=t;t++;);v; \\ _Anders Hellström_, Aug 16 2015
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 15 2000
%E a(9) corresponds to a probable prime, was discovered on Oct 22 2007. Trial factored to 1E11 with Fermat base 2 primality test. - _Paul Bourdelais_
%E a(10) corresponds to a probable prime, discovered by _Paul Bourdelais_, Feb 01 2010
%E a(11) corresponds to a probable prime, discovered by _Paul Bourdelais_, Aug 03 2015
%E a(12) corresponds to a probable prime, discovered by _Paul Bourdelais_, Sep 23 2020
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