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

1, 2, 2929, 5, 41459, 76, 21, 295, 2352527, 10, 963400369, 1162, 15, 68, 22082967607, 42, 144937, 217, 25, 1054, 1948397, 60, 14495, 266, 721, 28, 4343, 33, 193511, 52, 6884974839, 49, 1055, 48, 622699582951, 39806, 333, 44, 205, 70, 791, 460, 335, 725, 439889

Offset: 0

Author

Robert G. Wilson v, Dec 31 2002

Keywords

• nonn

Comments

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

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

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000 with -1 for large entries where a(n) has not yet been found, Nov 23 2016 [With 162 new terms, this supersedes the earlier table from Robert G. Wilson v et al.]
• Jan-Christoph Schlage-Puchta, C program
• Robert G. Wilson v et al., Table of n, a(n) for n = 0..10000 with -1 for those entries where a(n) has not yet been found

Crossrefs

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

Programs

Mathematica

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 = 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

Extensions

More terms from Don Reble, Jan 02 2003

a(14) conjectured by Max Alekseyev, Jun 17 2006

a(14) confirmed by Ryan Propper, Feb 03 2007

a(30) from Ryan Propper, Feb 03 2007

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

Corrections from Jon E. Schoenfield, Oct 10 2008

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

a(34), a(74), a(160) from Hagen von Eitzen, May 08, Jun 16 2009

a(254), a(310) from Daniel Morel, Sep 13, Sep 29 2009

Edited by Max Alekseyev, Feb 11 2012