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A128172
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Least k such that n^k mod k = n+1.
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18
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4700063497, 41459, 6821, 15853, 121129, 535, 36196439, 3827, 15084115509707, 8153, 20395, 5805311, 93929, 3736136819, 1343851, 7099195, 319, 559, 96641237093, 5053, 1535, 280517, 148731221, 869, 2062919, 17473, 803, 39259
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| a(36)=A178197(37) > 10^13. a(38)=A178199(39) > 10^13. [From Max Alekseyev, Feb 04 2012]
a(n)=k must be odd since n and a(n) are of opposite parity. The only way this can occur is if k is odd. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 12 2009]
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LINKS
| Hagen von Eitzen, Table of n, a(n) for n=2..35.
Robert G. Wilson v et al., Table of n, a(n) for n = 2..10000 with -1 for large entries where a(n) has not yet been found
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EXAMPLE
| a(2) = A036236(3) = 4700063497.
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MATHEMATICA
| t = Table[0, {10000}]; f[n_] := Block[{k = 1}, While[k < 2097153 && PowerMod[n, k, k] != n + 1, If[ Mod[k, 6] == 1, k += 4, k += 2]]; k]; Do[ If[ t[[n]] == 0, a = f@n; If[a < 2097153, t[[n]] = a; Print[{n, a}]]], {n, 10000}]; t [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 12 2009]
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CROSSREFS
| Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159, A128160.
Cf. A128149 = Least k such that n^k mod k = n-1.
Sequence in context: A172797 A199631 A124977 * A050259 A175568 A015384
Adjacent sequences: A128169 A128170 A128171 * A128173 A128174 A128175
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KEYWORD
| nonn,changed
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 17 2007
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EXTENSIONS
| a(15) = A128155(16) = 3736136819 and a(16) = A128156(17) = 1343851 found by Ryan Propper Feb 27-28 2007.
a(10),a(17),a(20),a(23)-a(24),a(26),a(30)-a(31),a(33)-a(35) determined. Tyler Cadigan (tylercadigan(AT)gmail.com), Feb 21 2009
Terms corrected by Hagen von Eitzen (math(AT)von-eitzen.de) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2009
Removed obsolete link to a-file duplicate - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2009
Edited and a(41) added by Max Alekseyev (maxale(AT)gmail.com), Feb 04 2012
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