A128366 a(n) = least k such that the remainder when 26^k is divided by k is n.

5, 3, 23, 6, 7, 10, 19, 9, 17, 18, 15, 92, 18881, 319, 36091, 20, 203, 94, 49, 21, 42395, 42, 17553, 326, 106709, 27, 2062919, 36, 14099, 34, 35, 46, 850984699, 214, 5847, 44, 341, 58, 377, 106, 105, 634, 301265879, 158, 93107, 90, 759, 176, 187, 69, 685, 78

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• nonn

Comments

If a(199) exists, a(199) >= 148000000000. - Zhuorui He, Jul 24 2025

Links

• Zhuorui He, Table of n, a(n) for n = 1..198 (first 152 terms from Robert G. Wilson v).
• Robert G. Wilson v, 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, A128363, A128364, A128365, 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; lst = {}; While[k < 1200000000, a = PowerMod[26, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]; If[a + 1 == k, AppendTo[lst, a]; Print@lst]]; k++ ]; lst (* Robert G. Wilson v, Jun 30 2009 *)

Extensions

a(27)-a(52) from Robert G. Wilson v, Jun 30 2009