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 A133857 Numbers n such that (18^n - 1)/17 is prime. 1
 2, 25667, 28807, 142031, 157051, 180181, 414269 (list; graph; refs; listen; history; text; internal format)
 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 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 Paul Bourdelais,Generalized Repunit Conjecture - Paul Bourdelais, Mar 12 2010 H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. 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^n-1)/17) \\ Charles R Greathouse IV, Jun 13 2017 CROSSREFS Cf. A128164 (Least k>2 such that (n^k-1)/(n-1) is prime). Cf. A084740 (Least k such that (n^k-1)/(n-1) is prime). Cf. A126589 (Numbers n>1 such that prime of the form (n^k-1)/(n-1) 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

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)