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%I #30 Dec 14 2016 20:10:35
%S 2,7,6,5,38,723,74,2592842671511,11,3827,14,717,34,59035,21,259,152,
%T 237,62,626131,30,169,58,25,56,1921,39,361,65,49,63010,287,48,55,46,
%U 63,932,3786791,69,69637,230,221,6707,1057,57,4907,253,681,148,393217991,70
%N a(n) = least k such that the remainder when 9^k is divided by k is n.
%H Fausto A. C. Cariboni, <a href="/A127817/a127817_2.txt">Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found</a>, Nov 21 2016 [With 202 new terms, this supersedes an earlier table of Robert G. Wilson v et al.]
%e For n=4, since 9^5 == 4 (mod 5) and 9^k is not congruent to 4 (mod k) for any k < 5, a(4) = 5. _Michael B. Porter_, Dec 10 2016
%p a127817 := [seq(0,j=1..nmax)] ; for k from 1 do n := modp(9^k,k) ; if n > 0 and n <= nmax then if op(n,a127817) = 0 then a127817 := subsop(n=k,a127817) ; print( op(1..50,a127817) ) ; fi; fi; od: # _R. J. Mathar_, Jul 16 2009
%t t = Table[0, {10000}]; k = 1; lst = {}; While[k < 4500000000, a = PowerMod[9, k, k]; If[ a<10001 && t[[a]]==0, t[[a]]=k; Print[{a,k}]]; k++ ]; t
%Y Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127818, A127819, A127820, A127821.
%K hard,nonn
%O 1,1
%A _Alexander Adamchuk_, Jan 30 2007
%E a(8) <= 2592842671511 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007
%E I changed the Mathematica coding to reflect the current limits _Robert G. Wilson v_, Jul 18 2009
%E Value for a(8) as suggested by J. K. Crump confirmed by _Hagen von Eitzen_, Jul 21 2009
%E Authorship of a-file corrected by _R. J. Mathar_, Aug 24 2009
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