A128149 Least k such that n^k mod k = n-1.

2929, 137243, 4769, 4021227877, 387497, 7342733, 2592842671511, 22963573117, 18659, 120593747, 13757837, 17651, 17149, 16584420001, 613024059983, 407, 39959, 559, 581831, 305197, 235, 459207143, 855782591, 106709, 17678421233, 240055, 11227

Offset: 3

Author

Alexander Adamchuk, Feb 16 2007

Keywords

• hard
• nonn

Examples

			a(3) = A078457(2) = 2929.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 3..41
• Robert G. Wilson v et al., Table of n, a(n) for n = 3..1000 with -1 for large entries where a(n) has not yet been found.

Crossrefs

Cf. A128150 = least k such that n^k mod k = (n-1)^2

Cf. A128172 = least k such that n^k mod k = n+1.

Cf. A128148, A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.

Cf. A128154, A128155, A128156, A128157, A128158, A128159, A128160, A128361, A128362, A128363, A128364, A128365, A128366, A128367, A128368, A128369, A129370, A128371, A128372.

Programs

Mathematica

t = Table[0, {10000}]; f[n_] := Block[{k = 1}, While[k < 2^23 && PowerMod[n, k, k] + 1 != n, If[ Mod[k, 6] == 1, k += 4, k += 2]]; k]; Do[ If[ t[[n]] == 0, a = f@n; If[a < 2^23, t[[n]] = a; Print[{n, a}]]], {n, 10000}] (* Robert G. Wilson v, Aug 15 2009 *)

Extensions

a(6) = A127816(5) = 4021227877 found by Ryan Propper, Feb 21 2007

More terms from Alexander Adamchuk, Feb 28 2007

a(9), a(10) from Hagen von Eitzen, Jul 31 2009

More terms from Robert G. Wilson v, Aug 15 2009

a(30), a(35), a(39), a(45) from Max Alekseyev, May 12 2012