%I A119678
%S A119678 3,14,137243,5,6821,10,57,124,35,18,2791496231,244,51,505,199534799,20,
%T A119678 30271293169,49,45,236,399531841,42,533,25,39,50,352957,36,995,98,33,
%U A119678 112,47503,55,42345881,44,2981,289,805,78,1019971289,25498,2121,212
%N A119678 a(n) = least k such that the remainder when 4^k is divided by k is n.
%C A119678 a(5^k-1) = 5^k.
%C A119678 a(n) > n.
%C A119678 Numbers n>1 such that a(n-1) = n are listed in A015950 = {1, 5, 25, 125, 
               205, 625, 1025, 2525, 3125, ...}
%C A119678 Numbers n such that n | 4^n + 1.
%H A119678 Ryan Propper, Feb 21 2007, <a href="b119678.txt">Table of n, a(n) for 
               n = 1..82</a>
%H A119678 Robert G. Wilson v, <a href="a119678.txt">Table of n, a(n) for n = 1..10000 
               with -1 for those entries where a(n) has not yet been found</a>
%t A119678 Do[k = 1; While[PowerMod[4, k, k] != n, k++ ]; Print[k], {n, 30}]
%t A119678 t = Table[0, {10000} ]; k = 1; While[ k < 5000000000, a = PowerMod[4, 
               k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ 
               ]; t
%Y A119678 Cf. A015950, A036236, A078457, A119679, A127816, A119715, A119714, A127817, 
               A127818, A127819, A127820, A127821.
%Y A119678 Sequence in context: A088334 A050645 A048568 this_sequence A096682 A009215 
               A088558
%Y A119678 Adjacent sequences: A119675 A119676 A119677 this_sequence A119679 A119680 
               A119681
%K A119678 nonn
%O A119678 1,1
%A A119678 Ryan Propper (rpropper(AT)stanford.edu), Jun 12 2006
%E A119678 a(11) <= 2791496231 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 
               10 2007
%E A119678 a(17) <= 140631956671 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 
               09 2007
%E A119678 a(53) <= 52134328061 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 
               06 2007
%E A119678 a(11) <= 29530730993777374794161795457107 from Max Alekseyev (maxale(AT)gmail.com), 
               Feb 04 2007
%E A119678 a(11) = 2791496231 from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 11 
               2007. Confirmed by Ryan Propper (rpropper(AT)stanford.edu), Feb 15 
               2007.
%E A119678 Extended through n = 82 by Ryan Propper (rpropper(AT)stanford.edu), Feb 
               21 2007
%E A119678 I expanded the search limits in the Mathematica coding Robert G. Wilson 
               v (rgwv(AT)rgwv.com), Jul 14 2009
%E A119678 Link corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 24 
               2009
%E A119678 a(83) = 3085807457009 = 113 * 331 * 82501603. a(87) > 10^13. [From Hagen 
               von Eitzen (math(AT)von-eitzen.de), Jul 27 2009]