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%I #10 Oct 02 2013 15:12:55
%S 5,34,213,68,4021227877,7,121129,14,69,26,767,51,6191,22,201,20,1919,
%T 33,169,44,39,1778,1926049,174,2673413,50,63,451,1257243481237,93,851,
%U 316,183,14809,1969,38,1362959,1826,177,289,65,87,5567,1252,57,1651,6403249
%N a(n) = least k >= 1 such that the remainder when 6^k is divided by k is n.
%C a(7^k-1) = 7^k.
%H Robert G. Wilson v, <a href="/A127816/a127816.txt">Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found</a>
%F a(7^k-1) = 7^k.
%t t = Table[0, {10000}]; k = 1; lst = {}; While[k < 5600000000, a = PowerMod[6, k, k]; If[ a<10001 && t[[a]]==0, t[[a]]=k; Print[{a,k}]]; k++ ]; t
%Y Cf. A036236, A078457, A119678, A119679, A119715, A119714, A127817, A127818, A127819, A127820, A127821.
%K hard,nonn
%O 1,1
%A _Alexander Adamchuk_, Jan 30 2007, Feb 05 2007
%E a(5) <= 20866130267 from _Max Alekseyev_, Feb 06 2007
%E a(5) <= 4021227877 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 10 2007
%E a(29) <= 1257243481237 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 09 2007
%E a(5) through a(28) from _Ryan Propper_, Feb 21 2007
%E I combined the two Mathematica codings into one and extended the search limits _Robert G. Wilson v_, Jul 16 2009
%E a(29) as conjectured by J. K. Crump confirmed by _Hagen von Eitzen_, Jul 21 2009
%E Corrected authorship of the a-file - _R. J. Mathar_, Aug 24 2009
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