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Search: id:A113516
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| A113516 |
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Least k such that n^k-n+1 is prime. |
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+0
2
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| 2, 2, 2, 5, 2, 2, 13, 2, 3, 3, 5, 2, 3, 2, 2, 11, 2, 3, 17, 2, 2, 17, 4, 2, 3, 9, 2, 33, 7, 3, 7, 4, 2, 3, 5, 67, 5, 2, 9, 3, 2, 4, 25, 3, 4, 5, 5, 24, 3, 2, 3, 21, 3, 2, 9, 3, 2, 11, 2, 5, 3, 2, 4, 19, 31, 2, 29, 4, 2, 3019, 2, 21, 51, 3, 2, 3, 2, 2, 9, 2, 169, 965, 3, 3, 29, 3, 2848, 9, 2, 2, 3
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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k can never be 8,14,20,... (k=2 mod 6) because, for those k, n^k-n+1 has the factor n^2-n+1, which is >1 for n>1. Using a result of Selmer, it can be shown that the polynomial x^k-x+1 is irreducible for all other k. The term a(93) is greater than 60000. Does a(n) exist for all n>1?
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MATHEMATICA
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Table[k=1; While[ !PrimeQ[n^k-n+1], k++ ]; k, {n, 2, 92}]
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CROSSREFS
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Cf. A113517 (smallest k such that k^n-k+1 is prime).
Sequence in context: A112659 A115281 A130155 this_sequence A120642 A095370 A046053
Adjacent sequences: A113513 A113514 A113515 this_sequence A113517 A113518 A113519
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 12 2006
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