A128172 Least k such that n^k mod k = n + 1.

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

Offset: 2

Author

Alexander Adamchuk, Feb 17 2007

Keywords

• nonn

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.]

Examples

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

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

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.

Programs

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 *)

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 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 a-file 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