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Search: id:A078457
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| A078457 |
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a(n) = least positive k such that the remainder when 3^k is divided by k is n. |
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36
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) > n.
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.
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
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LINKS
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Jan-Christoph Schlage-Puchta, C program
Robert G. Wilson v, Table of n, a(n) for n = 0..10000 with -1 for those entries where a(n) has not yet been found
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EXAMPLE
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a(664)=1363127889971; a(928)=900674663645 [From Mark Forbes (m.g.forbes(AT)ieee.org), Oct 25 2009]
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MATHEMATICA
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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
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CROSSREFS
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Cf. A015949, A036236, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.
Sequence in context: A114067 A109119 A002495 this_sequence A128148 A158348 A158904
Adjacent sequences: A078454 A078455 A078456 this_sequence A078458 A078459 A078460
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 31 2002
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Jan 02 2003
a(14)=22082967607 conjectured by Max Alekseyev (maxale(AT)gmail.com), Jun 17 2006; confirmed by Ryan Propper, Feb 03 2007
a(30) supplied by Ryan Propper (rpropper(AT)stanford.edu), Feb 03 2007
a(34) <= 405481796387612429411 from Max Alekseyev (maxale(AT)gmail.com), Feb 04 2007
a(34) <= 622699582951 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 10 2007
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
Corrections from Jon Schoenfield, Oct 10 2008
a(34) = 622699582951 from Hagen von EItzen (math(AT)von-eitzen.de), May 08 2009
a(74) = 337148405497007 = 13 * 13807 * 1878358277 [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 16 2009]
a(160) = 66190429538797 = 251177 * 263521061 [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 17 2009]
a(310) = 750413590189 = 229 * 2213 * 1480757 [From Daniel Morel (bazehu(AT)club-internet.fr), Sep 13 2009]
a(254) = 1191532143883 = 67 * 139 * 127942891 [From Daniel Morel (bazehu(AT)club-internet.fr), Sep 29 2009]
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