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Search: id:A084742
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| A084742 |
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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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| 3, 3, 3, 5, 3, 3, 0, 3, 5, 5, 5, 3, 7, 3, 3, 7, 3, 17, 5, 3, 3, 11, 7, 3, 11, 0, 3, 7, 139, 109, 0, 5, 3, 11, 31, 5, 5, 3, 53, 17, 3, 5, 7, 103, 7, 5, 5, 7, 1153, 3, 7, 21943, 7, 3, 37, 53, 3, 17, 3, 7, 11, 3, 0, 19, 7, 3, 757, 11, 3, 5, 3, 7, 13, 5, 3, 37, 3, 3, 5, 3, 293, 19, 7, 167, 7, 7, 709
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Conjecture: No entry is zero.
a(8)>1000 - Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 20 2003
When (n^k+1)/(n+1) is prime, k must be prime. As mentioned by Dubner and Granlund, when n is a power (greater than 2) of a prime, then (n^k+1)/(n+1) will usually be composite for all k, which is the case for n = 8, 27, 32 and 64. Some terms are only probable primes.
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LINKS
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H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
Eric Weisstein's World of Mathematics, Repunit
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EXAMPLE
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a(7)= 3 as (7^3 +1 )/(7+1) = 1 - 7 + 7^2 =43 is a prime.
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CROSSREFS
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Cf. A084741.
Cf. A065507 (for p=prime(n), the least prime q such that (p^q+1)/(p+1) is prime).
Sequence in context: A108688 A123371 A011277 this_sequence A049613 A002373 A103153
Adjacent sequences: A084739 A084740 A084741 this_sequence A084743 A084744 A084745
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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 22 2004
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