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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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+0
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
(list; graph; listen)
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OFFSET
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1,2
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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, ...}
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, Table of n, a(n) for n = 0..1000 with -1 for those entries where a(n) has not yet been found.
Jan-Christoph Schlage-Puchta, C program
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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: A139737 A012860 A036113 this_sequence A140351 A110492 A000876
Adjacent sequences: A078454 A078455 A078456 this_sequence A078458 A078459 A078460
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KEYWORD
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more,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 (maxal(AT)cs.ucsd.edu), 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 (maxal(AT)cs.ucsd.edu), Feb 04 2007
a(34) <= 622699582951 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 10 2007
a(1) 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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