%I A078457
%S A078457 1,2,2929,5,41459,76,21,295,2352527,10,963400369,1162,15,68,22082967607,
%T A078457 42,144937,217,25,1054,1948397,60,14495,266,721,28,4343,33,193511,52,
%U A078457 6884974839,49,1055,48,622699582951,39806,333,44,205,70,791,460,335,725,
               439889
%N A078457 a(n) = least positive k such that the remainder when 3^k is divided by 
               k is n.
%C A078457 a(n) > n.
%C A078457 Numbers n>1 such that a(n-1) = n are listed in A015949 = {1, 2, 10, 50, 
               250, 1250, 5050, 6250, ...}, i.e. numbers n such that n | 3^n + 1.
%C A078457 a(n) for which no value is currently known: n = 34, 74, 160, 254, 310, 
               394, 494, 634, 664, 730, 928, 974, 986, 1000, ..., . ... - a(0) to 
               a(1000) and a(56), a(110), a(128), a(134), a(187), a(286), a(348), 
               a(392), a(470), a(512), a(550), a(596), a(672), a(676), a(688), a(703), 
               a(716), a(748), a(772), a(784), a(860), a(980), ..., from Jan-Christoph 
               Schlage-Puchta (jcp(AT)mathematik.uni-freiburg.de), May 26 2008
%H A078457 Jan-Christoph Schlage-Puchta, <a href="a078457_C.txt">C program</a>
%H A078457 Robert G. Wilson v, <a href="a078457.txt">Table of n, a(n) for n = 0..10000 
               with -1 for those entries where a(n) has not yet been found</a>
%e A078457 a(664)=1363127889971; a(928)=900674663645 [From Mark Forbes (m.g.forbes(AT)ieee.org), 
               Oct 25 2009]
%t A078457 a = Table[0, {50}]; Do[b = PowerMod[3, n, n]; If[b < 51 && a[[b]] == 
               0, a[[b]] = n], {n, 1, 56*10^6}]; a
%t A078457 t = Table[0, {1000} ]; k = 1; While[ k < 200000000, a = PowerMod[3, k, 
               k]; If[a < 1001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; 
               t
%Y A078457 Cf. A015949, A036236, A119678, A119679, A127816, A119715, A119714, A127817, 
               A127818, A127819, A127820, A127821.
%Y A078457 Sequence in context: A114067 A109119 A002495 this_sequence A128148 A158348 
               A158904
%Y A078457 Adjacent sequences: A078454 A078455 A078456 this_sequence A078458 A078459 
               A078460
%K A078457 nonn
%O A078457 0,2
%A A078457 Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 31 2002
%E A078457 More terms from Don Reble (djr(AT)nk.ca), Jan 02 2003
%E A078457 a(14)=22082967607 conjectured by Max Alekseyev (maxale(AT)gmail.com), 
               Jun 17 2006; confirmed by Ryan Propper, Feb 03 2007
%E A078457 a(30) supplied by Ryan Propper (rpropper(AT)stanford.edu), Feb 03 2007
%E A078457 a(34) <= 405481796387612429411 from Max Alekseyev (maxale(AT)gmail.com), 
               Feb 04 2007
%E A078457 a(34) <= 622699582951 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 
               10 2007
%E A078457 Table of a(n) up to n =1000, including values for a(56), a(110), a(128), 
               a(134), a(187), a(286), a(348), a(392), a(470), a(512), a(550), a(596), 
               a(672), a(676), a(688), a(703), a(716), a(748), a(772), a(784), a(860), 
               a(980), ..., from Jan-Christoph Schlage-Puchta (jcp(AT)mathematik.uni-freiburg.de), 
               May 26 2008
%E A078457 Corrections from Jon Schoenfield, Oct 10 2008
%E A078457 a(34) = 622699582951 from Hagen von EItzen (math(AT)von-eitzen.de), May 
               08 2009
%E A078457 a(74) = 337148405497007 = 13 * 13807 * 1878358277 [From Hagen von Eitzen 
               (math(AT)von-eitzen.de), Jun 16 2009]
%E A078457 a(160) = 66190429538797 = 251177 * 263521061 [From Hagen von Eitzen (math(AT)von-eitzen.de), 
               Jun 17 2009]
%E A078457 a(310) = 750413590189 = 229 * 2213 * 1480757 [From Daniel Morel (bazehu(AT)club-internet.fr), 
               Sep 13 2009]
%E A078457 a(254) = 1191532143883 = 67 * 139 * 127942891 [From Daniel Morel (bazehu(AT)club-internet.fr), 
               Sep 29 2009]