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

3,1

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.

Example

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

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 *)

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.

Sequence in context: A054831 A127490 A237079 * A276671 A251233 A251983

Adjacent sequences: A128146 A128147 A128148 * A128150 A128151 A128152

Keyword

hard,nonn

Author

Alexander Adamchuk, Feb 16 2007

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

Status

approved