A127816 a(n) = least k >= 1 such that the remainder when 6^k is divided by k is n.

5, 34, 213, 68, 4021227877, 7, 121129, 14, 69, 26, 767, 51, 6191, 22, 201, 20, 1919, 33, 169, 44, 39, 1778, 1926049, 174, 2673413, 50, 63, 451, 1257243481237, 93, 851, 316, 183, 14809, 1969, 38, 1362959, 1826, 177, 289, 65, 87, 5567, 1252, 57, 1651, 6403249

Offset: 1

Author

Alexander Adamchuk, Jan 30 2007, Feb 05 2007

Keywords

• hard
• nonn

Comments

a(7^k-1) = 7^k.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found

Crossrefs

Cf. A036236, A078457, A119678, A119679, A119715, A119714, A127817, A127818, A127819, A127820, A127821.

Programs

Mathematica

t = Table[0, {10000}]; k = 1; lst = {}; While[k < 5600000000, a = PowerMod[6, k, k]; If[ a<10001 && t[[a]]==0, t[[a]]=k; Print[{a,k}]]; k++ ]; t

Formula

a(7^k-1) = 7^k.

Extensions

a(5) from Joe K. Crump confirmed and a(6)-a(28) added by Ryan Propper, Feb 21 2007

I combined the two Mathematica codings into one and extended the search limits. - Robert G. Wilson v, Jul 16 2009

a(29) as conjectured by J. K. Crump confirmed by Hagen von Eitzen, Jul 21 2009

Corrected authorship of the a-file - R. J. Mathar, Aug 24 2009