%I A128172
%S A128172 4700063497,41459,6821,15853,121129,535,36196439,3827,15084115509707,
%T A128172 8153,20395,5805311,93929,3736136819,1343851,7099195,319,559,
%U A128172 96641237093,5053,1535,280517,148731221,869,2062919,17473,803,39259
%N A128172 Least k such that n^k (mod k) = n+1.
%C A128172 a(11)-a(14) = {8153, 20395, 5805311, 93929}. a(18)-a(19) = {319, 559}. 
               a(21)-a(22) = {5053, 1535}. a(25) = 869.
%C A128172 a(27)-a(29) = {17473, 803, 39259}. a(32) = 95. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Feb 17 2007
%C A128172 a(15) = A128155(16) = 3736136819 and a(16) = A128156(17) = 1343851 found 
               by Ryan Propper Feb 27-28 2007.
%C A128172 First term currently unknown is a(36) >= 41*10^10. [From Tyler Cadigan 
               (tylercadigan(AT)gmail.com), Feb 21 2009]
%C A128172 a(n)=k must be odd since n and a(n) are of opposite parity. The only 
               way this can occur is if k is odd. [From Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Aug 12 2009]
%H A128172 Hagen von Eitzen, <a href="b128172.txt">Table of n, a(n) for n=2..35</
               a>.
%H A128172 Robert G. Wilson v, <a href="a128172.txt">Table of n, a(n) for n = 2..10000 
               with -1 for large entries where a(n) has not yet been found</a> [From 
               Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 12 2009]
%e A128172 a(2) = A036236(3) = 4700063497.
%t A128172 t = Table[0, {10000}]; f[n_] := Block[{k = 1}, While[k < 2097153 && PowerMod[n, 
               k, k] != n + 1, If[ Mod[k, 6] == 1, k += 4, k += 2]]; k]; Do[ If[ 
               t[[n]] == 0, a = f@n; If[a < 2097153, t[[n]] = a; Print[{n, a}]]], 
               {n, 10000}]; t [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 12 
               2009]
%Y A128172 Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, 
               A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, 
               A128158, A128159, A128160. Cf. A128149 = Least k such that n^k (mod 
               k) = n-1.
%Y A128172 Sequence in context: A092776 A034916 A124977 this_sequence A050259 A015384 
               A072018
%Y A128172 Adjacent sequences: A128169 A128170 A128171 this_sequence A128173 A128174 
               A128175
%K A128172 nonn
%O A128172 2,1
%A A128172 Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 17 2007
%E A128172 a(10),a(17),a(20),a(23)-a(24),a(26),a(30)-a(31),a(33)-a(35) determined. 
               Tyler Cadigan (tylercadigan(AT)gmail.com), Feb 21 2009
%E A128172 Terms corrected by Hagen von Eitzen (math(AT)von-eitzen.de) and R. J. 
               Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2009
%E A128172 Removed obsolete link to a-file duplicate - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 24 2009