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A133857
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Numbers k such that (18^k - 1)/17 is prime.
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1
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Eric Weisstein's World of Mathematics, Repunit.
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EXAMPLE
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PROG
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CROSSREFS
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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).
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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