A128363 a(n) = least k such that the remainder when 23^k is divided by k is n.

2, 3, 5, 19, 262, 17, 58, 9, 10, 13, 14, 55, 86, 12153, 514, 111823, 95, 25, 30, 12147, 68, 235, 29, 280517, 56, 27, 502, 16805, 51, 49, 166, 35, 62, 1837, 38, 977969, 82, 39, 1370, 289, 122, 9822698929535, 65, 133, 697, 161, 303, 19445, 50, 147, 259, 1247

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• nonn

Links

• Max Alekseyev et al., Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found

Crossrefs

Cf. A128361, A128362, A128364, A128365, A128366, A128367, A128368, A128369, A129370, A128371, A128372.

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159, A128160.

Cf. A128149, A128150, A128172.

Programs

Mathematica

t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[23, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 04 2009 *)
Table[Module[{k=1},While[PowerMod[23,k,k]!=n,k++];k],{n,35}] (* The program generates the first 35 terms of the sequence. *) (* Harvey P. Dale, Jul 18 2025 *)

Extensions

a(42), a(64) from Hagen von Eitzen, Aug 04 2009

a(750), a(770), a(234), a(274), a(406), a(600), a(610), a(754) from Daniel Morel, May 31, Aug 24, Sep 20 2010

a(84) from Max Alekseyev, Apr 13 2012