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A133857
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Numbers n such that (18^n - 1)/17 is prime.
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0
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OFFSET
| 1,1
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COMMENTS
| a(2) = 25667 and a(3) = 28807 found by Henri Lifchitz 09/2007.
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. [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), 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=.6667. [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 17 2010]
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REFERENCES
| H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
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LINKS
| Henri & Renaud Lifchitz, PRP Records.
Eric Weisstein's World of Mathematics, Repunit.
Paul Bourdelais,Generalized Repunit Conjecture [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 12 2010]
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EXAMPLE
| a(1) = A084740(18) = 2,
a(2) = A128164(18) = 25667.
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PROG
| (Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 17 2010]
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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: A123692 A132942 A131558 * A153912 A047076 A176721
Adjacent sequences: A133854 A133855 A133856 * A133858 A133859 A133860
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KEYWORD
| hard,more,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 28 2007
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EXTENSIONS
| a(4)=142031 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 12 2010
a(5)=157051 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 15 2010
a(6)=180181 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 17 2010
a(6)=180181 was previously discovered by Andy Steward 04/2007 in the form of the cyclotomic number Phi(180181,18). Entry edited by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 23 2010
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