Search: id:A058013
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%I A058013
%S A058013 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,
%T A058013 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,
%U A058013 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
%N A058013 Smallest prime p such that (n+1)^p - n^p is prime.
%C A058013 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
%C A058013 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
%C A058013 a((p-1)/2) = 2 for odd primes p. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Dec 01 2006
%H A058013 <a href="http://groups.yahoo.com/group/primeform/">User group for PFGW 
               & PrimeForm programs.</a>
%t A058013 Do[ k = 1; While[ !PrimeQ[ (n + 1)^Prime[ k ] - n^Prime[ k ] ], k++ ]; 
               Print[ Prime[ k ] ], {n, 1, 100} ]
%Y A058013 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).
%Y A058013 Sequence in context: A142240 A048288 A050677 this_sequence A031356 A024676 
               A093429
%Y A058013 Adjacent sequences: A058010 A058011 A058012 this_sequence A058014 A058015 
               A058016
%K A058013 nonn
%O A058013 1,1
%A A058013 Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 13 2000
%E A058013 More terms from T. D. Noe (noe(AT)sspectra.com), Dec 05 2005

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