A119714 a(n) is the least k such that the remainder when 8^k is divided by k is n.

7, 3, 5, 6, 39, 58, 7342733, 9, 36196439, 18, 501, 26, 13607, 249, 119, 20, 33, 25, 866401, 22, 533, 35, 185, 50, 196673, 27, 1843, 36, 69, 34, 551, 55, 3773365, 110, 159, 116, 355, 237, 8401, 52, 471, 81815, 85, 261, 11783479, 3258, 93, 92, 1885511821439

Offset: 1

Author

Ryan Propper, Jun 12 2006

Keywords

• hard
• nonn

Comments

a(61) = 1802190094793 = 11 * 59 * 17839 * 155663. - Hagen von Eitzen, Jul 28 2009

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, A127816, A119715, A127817, A127818, A127819, A127820, A127821.

Programs

Mathematica

Do[k = 1; While[PowerMod[8, k, k] != n, k++ ]; Print[k], {n, 48}]
t = Table[0, {10000}]; k = 1; lst = {}; While[k < 4300000000, a = PowerMod[8, k, k]; If[ a<10001 && t[[a]]==0, t[[a]]=k; Print[{a,k}]]; k++ ]; t (* Mathematica coding extended to reflect the new search limits as posted in the a-file by Robert G. Wilson v, Jul 17 2009 *)

Extensions

a(49) from Hagen von Eitzen, Jul 24 2009