%I A125713
%S A125713 3,3,3,3,5,3,7,7,3,3,3,17,3,3,43,5,3,1607,5,19,127,229,3,3,3,13,3,3,149,
%T A125713 3,5,3,23,3,5,83,3,3,37,7,3,3,37,5,3,5,58543,3,3,7,29,3,479,5,3,19,5,3,
%U A125713 4663,54517,17,3,3,5,7,3,3,17,11,47,61,19,23,3,5,19,7,5,7,3,3,331,41
%N A125713 Smallest odd prime p such that (n+1)^p - n^p is prime.
%C A125713 Corresponding smallest primes of the form (n+1)^p - n^p, where p = a(n) 
               is an odd prime, are listed in A121091(n+1) = {7, 19, 37, 61, 4651, 
               127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, 
               ...}. a(n) = A058013(n) for n = {4, 7, 10, 12, 13, 16, 17, 19, 22, 
               24, 25, 27, 28, 31, ...} = A047845(n) = (n-1)/2, where n runs through 
               odd nonprimes (A014076), for n>1. a(97) = 7. a(99)-a(112) = {5, 43, 
               5, 13, 7, 5, 3, 6529, 59, 3, 5, 5, 113, 5}. a(114) = 139. a(117)-a(129) 
               = {7, 13, 3, 5, 5, 7, 3, 5167, 3, 41, 59, 3, 3}. a(131) = 101. a(n) 
               is currently unknown for n = {113, 115, 116, 130, 132, ...}.
%C A125713 a(96) = 1307, a(98) = 709.
%Y A125713 Cf. A058013 = Smallest prime p such that (n+1)^p - n^p is prime. Cf. 
               A065913 = Smallest prime of form (n+1)^k - n^k. Cf. A121091 = Smallest 
               nexus prime of the form n^p - (n-1)^p, where p is odd prime. Cf. 
               A047845, A014076.
%Y A125713 Cf. A062585 = numbers n such that k^n - (k-1)^n is prime, where k is 
               19. Cf. A000043, A057468, A059801, A059802, A062572-A062666.
%Y A125713 Sequence in context: A046074 A068048 A056206 this_sequence A162220 A118911 
               A111756
%Y A125713 Adjacent sequences: A125710 A125711 A125712 this_sequence A125714 A125715 
               A125716
%K A125713 hard,nonn
%O A125713 1,1
%A A125713 Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 01 2006, Feb 15 2007