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%I M3767 N1537 #57 May 05 2020 02:04:10
%S 5,7,19,31,53,67,293,641,2137,3011,268207,1600787
%N Numbers n such that (10^n + 1)/11 is a prime.
%C The a(10) to a(11) gap represents the largest relative gap seen so far in searching repunits with bases between -12 and 12. On average, there should have been 4 more primes added to this sequence by a(11), instead of just 1. - _Paul Bourdelais_, Feb 11 2010
%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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%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>, 2009.
%H J. Brillhart, <a href="/A001562/a001562.pdf">Letter to N. J. A. Sloane, Aug 08 1970</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="http://www.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 Select[Range[3000], PrimeQ[(10^# + 1) / 11] &] (* _Vincenzo Librandi_, Oct 29 2017 *)
%o (PARI) isok(n) = (denominator(p=(10^n+1)/11)==1) && isprime(p); \\ _Michel Marcus_, Oct 29 2017
%Y Equals 2*A054416 + 1.
%Y Odd terms of A309358.
%K nonn,hard,more
%O 1,1
%A _N. J. A. Sloane_
%E a(11) corresponds to a probable prime discovered by _Paul Bourdelais_, Feb 11 2010
%E a(12) corresponds to a probable prime discovered by _Paul Bourdelais_, May 04 2020
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