%I
%S 2,25667,28807,142031,157051,180181,414269
%N Numbers n such that (18^n  1)/17 is prime.
%C Repunits in base 18 are off to a slow start compared with all the repunits in bases from 20 to 20. There are only 4 repunit primes in base 18 with exponents searched up to 150,000 while most other bases have 710 by then. Even after scaling the rate by logb logb, this is relatively low.  _Paul Bourdelais_, Mar 12 2010
%C With the discovery of a(6), this sequence in base 18 repunits is converging nicely to a rate close to Euler's constant with G=0.6667.  _Paul Bourdelais_, Mar 17 2010
%C With the discovery of a(7), G=0.54789, which is very close to the expected constant 0.56145948 mentioned in the Generalized Repunit Conjecture below.  _Paul Bourdelais_, Dec 08 2014
%H Paul Bourdelais,<a href="https://listserv.nodak.edu/cgibin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">Generalized Repunit Conjecture</a>  _Paul Bourdelais_, Mar 12 2010
%H H. Dubner, <a href="http://dx.doi.org/10.1090/S00255718199311852439">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927930.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=%2818%5Ex1%29%2F17&action=Search">PRP Records</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>.
%e a(1) = A084740(18) = 2,
%e a(2) = A128164(18) = 25667.
%o (PARI) is(n)=ispseudoprime((18^n1)/17) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A128164 (Least k>2 such that (n^k1)/(n1) is prime). Cf. A084740 (Least k such that (n^k1)/(n1) is prime). Cf. A126589 (Numbers n>1 such that prime of the form (n^k1)/(n1) does not exist for k>2).
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Sep 28 2007
%E a(2) = 25667 and a(3) = 28807 found by Henri Lifchitz, Sep 2007
%E a(4) corresponds to a probable prime discovered by _Paul Bourdelais_, Mar 12 2010
%E a(5) corresponds to a probable prime discovered by _Paul Bourdelais_, Mar 15 2010
%E a(6)=180181, previously discovered by Andy Steward in April 2007 in the form of the cyclotomic number Phi(180181,18), added by _Paul Bourdelais_, Mar 23 2010
%E a(7) corresponds to a probable prime discovered by _Paul Bourdelais_, Dec 08 2014
