

A133857


Numbers n such that (18^n  1)/17 is prime.


1




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 710 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 in 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

Table of n, a(n) for n=1..7.
Paul Bourdelais,Generalized Repunit Conjecture  Paul Bourdelais, Mar 12 2010
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930.
Henri & Renaud Lifchitz, PRP Records.
Eric Weisstein's World of Mathematics, Repunit.


EXAMPLE

a(1) = A084740(18) = 2,
a(2) = A128164(18) = 25667.


PROG

(PARI) is(n)=ispseudoprime((18^n1)/17) \\ Charles R Greathouse IV, Jun 13 2017


CROSSREFS

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).
Sequence in context: A132942 A237521 A131558 * A232869 A153912 A247790
Adjacent sequences: A133854 A133855 A133856 * A133858 A133859 A133860


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


STATUS

approved



