

A128172


Least k such that n^k mod k = n + 1.


19



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
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OFFSET

2,1


COMMENTS

a(n)=k must be odd since n and n+1 are of opposite parity. The only way this can occur is if k is odd.  Robert G. Wilson v, Aug 12 2009 [Comment corrected by Fausto A. C. Cariboni, Nov 20 2016.]


LINKS

Max Alekseyev, Table of n, a(n) for n = 2..43
Fausto A. C. Cariboni, Table of n, a(n) for n = 2..10000 with 1 for large entries where a(n) has not yet been found, Dec 24 2016 [With 1772 new terms, this supersedes the earlier table from Robert G. Wilson v et al.]
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


EXAMPLE

a(2) = A036236(3) = 4700063497.


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 (* Robert G. Wilson v, Aug 12 2009 *)


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 A249972 A233494
Adjacent sequences: A128169 A128170 A128171 * A128173 A128174 A128175


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Feb 17 2007


EXTENSIONS

a(15) = A128155(16) = 3736136819 and a(16) = A128156(17) = 1343851 found by Ryan Propper, Feb 2728 2007
a(10), a(17), a(20), a(23)a(24), a(26), a(30)a(31), a(33)a(35) determined by Tyler Cadigan (tylercadigan(AT)gmail.com), Feb 21 2009
Terms corrected by Hagen von Eitzen and R. J. Mathar, Aug 05 2009
Obsolete link to afile duplicate removed by R. J. Mathar, Aug 24 2009
Edited and a(36), a(38), a(41), a(48), a(49) added by Max Alekseyev, Feb 04, Mar 25, May 07 2012


STATUS

approved



