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Search: id:A084740
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| A084740 |
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Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists. |
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+0
7
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| 2, 3, 2, 3, 2, 5, 3, 0, 2, 17, 2, 5, 3, 3, 2, 3, 2, 19, 3, 3, 2, 5, 3, 0, 7, 3, 2, 5, 2, 7, 0, 3, 13, 313, 2, 13, 3, 349, 2, 3, 2, 5, 5, 19, 2, 127, 19, 0, 3, 4229, 2, 11, 3, 17, 7, 3, 2, 3, 2, 7, 3, 5, 0, 19, 2, 19, 5, 3, 2, 3, 2, 5, 5, 3, 41, 3, 2, 5, 3, 0, 2, 5, 17, 5, 11, 7, 2, 3, 3, 4421, 439
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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When (n^k-1)/(n-1) is prime, k must be prime. As mentioned by Dubner, when n is a power (greater than 1) of a prime, then (n^k-1)/(n-1) will usually be composite for all k, which is the case for n = 9, 25, 32, 49, 64, and 81. - T. D. Noe (noe(AT)sspectra.com), Jan 30 2004
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REFERENCES
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H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
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LINKS
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Andy Steward, Titanic Prime Generalized Repunits
Eric Weisstein's World of Mathematics, Repunit
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EXAMPLE
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a(7) = 5 as (7^5 - 1 )/(7 - 1) = 2801 = 1 + 7 + 7^2 + 7^3 + 7^4 is a prime but no smaller partial sum yields a prime.
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CROSSREFS
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Cf. A084738, A065854 (for p=prime(n), the least prime q such that (p^q-1)/(p-1) is prime).
Adjacent sequences: A084737 A084738 A084739 this_sequence A084741 A084742 A084743
Sequence in context: A086757 A046215 A057019 this_sequence A077199 A064652 A077600
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 15 2003
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 23 2004
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