OFFSET
1,1
COMMENTS
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 7-10 by then. Even after scaling the rate by logb logb, this is relatively low. - Paul Bourdelais, Mar 12 2010
With the discovery of a(6), this sequence of base-18 repunits is converging nicely to a rate close to Euler's constant with G=0.6667. - Paul Bourdelais, Mar 17 2010
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
LINKS
Paul Bourdelais, Generalized Repunit Conjecture - Paul Bourdelais, Mar 12 2010
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
Henri and Renaud Lifchitz, PRP Records.
Eric Weisstein's World of Mathematics, Repunit.
PROG
(PARI) is(n)=ispseudoprime((18^n-1)/17) \\ Charles R Greathouse IV, Jun 13 2017
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Sep 28 2007
EXTENSIONS
a(2) = 25667 and a(3) = 28807 found by Henri Lifchitz, Sep 2007
a(4) corresponds to a probable prime discovered by Paul Bourdelais, Mar 12 2010
a(5) corresponds to a probable prime discovered by Paul Bourdelais, Mar 15 2010
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
a(7) corresponds to a probable prime discovered by Paul Bourdelais, Dec 08 2014
a(8) from Paul Bourdelais, Dec 02 2021
STATUS
approved