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A078457 a(n) = least positive k such that the remainder when 3^k is divided by k is n. 47

%I

%S 1,2,2929,5,41459,76,21,295,2352527,10,963400369,1162,15,68,

%T 22082967607,42,144937,217,25,1054,1948397,60,14495,266,721,28,4343,

%U 33,193511,52,6884974839,49,1055,48,622699582951,39806,333,44,205,70,791,460,335,725,439889

%N a(n) = least positive k such that the remainder when 3^k is divided by k is n.

%C a(n) > n. Numbers n such that a(n-1) = n are listed in A015949.

%C a(n) for which no value is currently known: n = 394, 494, 634, 730, 974, 986, 1000, ...

%H Fausto A. C. Cariboni, <a href="/A078457/a078457_2.txt">Table of n, a(n) for n = 0..10000 with -1 for large entries where a(n) has not yet been found</a>, Nov 23 2016 [With 162 new terms, this supersedes the earlier table from Robert G. Wilson v et al.]

%H Jan-Christoph Schlage-Puchta, <a href="/A078457/a078457_C.txt">C program</a>

%H Robert G. Wilson v et al., <a href="/A078457/a078457_1.txt">Table of n, a(n) for n = 0..10000 with -1 for those entries where a(n) has not yet been found</a>

%t 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 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 Cf. A015949, A036236, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Dec 31 2002

%E More terms from _Don Reble_, Jan 02 2003

%E a(14) conjectured by _Max Alekseyev_, Jun 17 2006

%E a(14) confirmed by _Ryan Propper_, Feb 03 2007

%E a(30) from _Ryan Propper_, Feb 03 2007

%E 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 Corrections from _Jon E. Schoenfield_, Oct 10 2008

%E a(664), a(928) from Mark Forbes (m.g.forbes(AT)ieee.org), Oct 25 2009

%E a(34), a(74), a(160) from _Hagen von Eitzen_, May 08, Jun 16 2009

%E a(254), a(310) from _Daniel Morel_, Sep 13, Sep 29 2009

%E Edited by _Max Alekseyev_, Feb 11 2012

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)