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Search: id:A103794
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| A103794 |
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Smallest number b such that b^Prime(n)-(b-1)^Prime(n) is prime. |
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2
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| 2, 2, 2, 2, 6, 2, 2, 2, 6, 3, 2, 40, 7, 5, 13, 3, 3, 2, 7, 18, 47, 8, 6, 2, 26, 3, 42, 2, 13, 8, 2, 8, 328, 8, 9, 45, 27, 13, 76, 15, 52, 111, 5, 15, 50, 287, 16, 5, 40, 23, 110, 368, 23, 68, 28, 96, 81, 150, 3, 143, 4, 12, 403, 4, 45, 11, 83, 21, 96, 5, 109, 350, 128, 304, 38, 4, 163
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: sequence is defined for all positive indices.
For p=prime(n), Eisenstein's irreducibility criterion can be used to show that the polynomial (x+1)^p-x^p is irreducible, which is a necessary (but not sufficient) condition for a(n) to exist. - T. D. Noe (noe(AT)sspectra.com), Dec 05 2005
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EXAMPLE
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2^Prime(1)-1^Prime(1)=3 is prime, so a(1)=2;
2^Prime(5)-1^Prime(5)=2047 has a factor of 23;
...
6^Prime(5)-5^Prime(5)=313968931 is prime, so a(5)=6;
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MATHEMATICA
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Do[p=Prime[k]; n=2; nm1=n-1; cp=n^p-nm1^p; While[ !PrimeQ[cp], n=n+1; nm1=n-1; cp=n^p-nm1^p]; Print[n], {k, 1, 200}]
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CROSSREFS
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Cf. A103795, A066180, A058013.
Sequence in context: A098789 A079894 A114005 this_sequence A073124 A070877 A130754
Adjacent sequences: A103791 A103792 A103793 this_sequence A103795 A103796 A103797
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KEYWORD
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nonn
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AUTHOR
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Lei Zhou (lzhou5(AT)emory.edu), Feb 24 2005
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