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Search: id:A126589
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| A126589 |
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Numbers n>1 such that prime of the form (n^k-1)/(n-1) does not exist for k>2; or A128164(n) = 0. |
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+0
2
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| 4, 9, 16, 25, 32, 36, 49, 64, 81, 100, 121, 125, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) appears to be a union of the perfect squares k^2 for k>1 with the powers of primes p^k for k>1 with some exceptions, such as 2^3, 3^3, 2^7, etc.
The perfect powers except those of the form n^(p^m) where p and (n^(p^(m+1))-1)/(n^(p^m)-1) are primes, p>2 and m>=1. [From Max Alekseyev (maxale(AT)gmail.com), Mar 09 2009]
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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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Eric Weisstein's World of Mathematics, Repunit.
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EXAMPLE
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A128164(n) begins with offset 2 {3, 3, 0, 3, 3, 5, 3, 0, 19, 17, 3, 5, 3, 3, 0, 3, ...}.
Thus a(1) = 4, a(2) = 9, a(3) = 16.
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CROSSREFS
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Cf. A128164 = Least k>2 such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists. Cf. A084738, A065854, A084740 = Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists. Cf. A084741, A065507, A084742 = Least k such that (n^k+1)/(n+1) is prime, or 0 if no such prime exists.
Sequence in context: A061077 A086132 A010433 this_sequence A010409 A010457 A004120
Adjacent sequences: A126586 A126587 A126588 this_sequence A126590 A126591 A126592
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Mar 13 2007
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EXTENSIONS
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Extended by Max Alekseyev (maxale(AT)gmail.com), Mar 09 2009
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