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Search: id:A058013
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| A058013 |
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Smallest prime p such that (n+1)^p - n^p is prime. |
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+0
5
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| 2, 2, 2, 3, 2, 2, 7, 2, 2, 3, 2, 17, 3, 2, 2, 5, 3, 2, 5, 2, 2, 229, 2, 3, 3, 2, 3, 3, 2, 2, 5, 3, 2, 3, 2, 2, 3, 3, 2, 7, 2, 3, 37, 2, 3, 5, 58543, 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 4663, 54517, 17, 3, 2, 5, 2, 3, 3, 2, 2, 47, 61, 19, 23, 2, 2, 19, 7, 2, 7, 3, 2, 331, 2, 179, 5, 2, 5, 3, 2, 2, 3, 17, 3
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The terms a(47) and a(60) [were] unknown. The sequence continues at a(48): 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 4663, a(60)=?, continued at a(61): 17, 3, 2, 5, 2, 3, 3, 2, 2, 47, 61, 19, 23, 2, 2, 19, 7, 2, 7, 3, 2, 331, 2, 179, 5, 2, 5, 3, 2, 2, 3, 17, 3, 61, 2, 2, 7, 2, 2 - Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 27 2004
In September and November 2005, Jean-Louis Charton found a(60)=54517 and a(47)=58543, respectively. Earlier, Mike Oakes found a(106)=7639 and a(124)=5839. All these large values of a(n) yield probable primes. - T. D. Noe (noe(AT)sspectra.com), Dec 05 2005, Sep 18 2008
a((p-1)/2) = 2 for odd primes p. - Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 01 2006
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LINKS
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User group for PFGW & PrimeForm programs.
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MATHEMATICA
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Do[ k = 1; While[ !PrimeQ[ (n + 1)^Prime[ k ] - n^Prime[ k ] ], k++ ]; Print[ Prime[ k ] ], {n, 1, 100} ]
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CROSSREFS
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Cf. A065913 (smallest prime of form (n+1)^k-n^k), A103794 (least b such that b^prime(n)-(b-1)^prime(n) is prime).
Sequence in context: A142240 A048288 A050677 this_sequence A031356 A024676 A093429
Adjacent sequences: A058010 A058011 A058012 this_sequence A058014 A058015 A058016
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 13 2000
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Dec 05 2005
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