A128371 a(n) = least k such that the remainder when 31^k is divided by k is n.

2, 29, 7, 29787, 13, 113413, 51, 23, 11, 3309, 38, 19, 21, 17, 22, 115, 118, 37237, 261, 60212617, 94, 29769, 134, 51205605391, 26, 35, 209, 549, 466, 1558391, 37, 5033228393, 58, 39, 926, 565, 57, 1561, 922, 119, 46, 2512157, 111, 949, 76, 85

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found [Superseded by Cariboni table]
• Fausto A. C. Cariboni, Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found, Sep 14 2016 [With 123 new terms, this supersedes the earlier table from Robert G. Wilson v et al.]

Crossrefs

Cf. A128361, A128362, A128363, A128364, A128365, A128366, A128367, A128368, A129369, A128370, 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 < 4750000000, a = PowerMod[31, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 06 2009 *)

Extensions

More terms from Ryan Propper, Mar 24 2007

a(494) = 14353729267 = 64609 * 222163. a(498) = 9547024387, a(540) = 29711794103. - Daniel Morel, Jun 17 2010. a(618) = 15150617101, a(750) = 13728669221. - Daniel Morel, Jun 28 2010