A128149
Least k such that n^k mod k = n-1.
Original entry on oeis.org
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
a(3) = A078457(2) = 2929.
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.
-
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 *)
A128150
Least k such that n^k mod k = (n-1)^2, or 0 if no such k exists.
Original entry on oeis.org
0, 41459, 35, 9569200211, 2673413, 10596486211, 1885511821439, 235, 12722173, 1971782729, 133617287, 14873, 1465, 1606870609, 4247, 129015968122421, 526673, 835, 1079115301, 12148589879, 12351683, 36947690849, 6385, 5809
Offset: 2
a(2) = A036236(1) = 0,
a(3) = A078457(2^2) = 41459,
a(4) = A119678(3^2) = 35,
a(5) = A119679(4^2) = 9569200211,
a(6) = A127816(5^2) = 2673413,
a(7) = A119715(6^2) = 10596486211,
a(8) = A119714(7^2) = 1885511821439,
a(9) = A127817(8^2) = 235,
a(10) = A127818(9^2) = 12722173,
a(11) = A127819(100) = 1971782729,
a(12) = A127820(121) = 133617287,
a(13) = A127821(144) = 14873,
a(14) = A128154(169) = 1465,
a(15) = A128155(196) = 1606870609,
a(16) = A128156(225) = 4247,
a(17) = A128157(256) = 129015968122421,
a(18) = A128158(289) = 526673,
a(19) = A128159(324) = 835,
a(20) = A128160(361) = 1079115301,
a(21) = A128361(400) = 12148589879,
a(22) = A128362(441) = 12351683,
a(23) = A128363(484) = 36947690849,
a(24) = A128364(529) = 6385,
a(25) = A128365(576) = 5809,
a(26) = A128366(625) > 10^15,
a(27) = A128367(676) = 299651,
a(28) = A128368(729) > 10^14,
a(29) = A128369(784) = 2645,
a(30) = A128370(841) = 13633321649263,
a(31) = A128371(900) = 1051624907,
a(32) = A128372(961) = 725521, etc.
Cf.
A128148,
A128149,
A128172,
A036236,
A078457,
A119678,
A119679,
A127816,
A119715,
A119714,
A127817,
A127818,
A127819,
A127820,
A127821,
A128154,
A128155,
A128156,
A128157,
A128158,
A128159,
A128160,
A128361,
A128362,
A128363,
A128364,
A128365,
A128366,
A128367,
A128368,
A128369,
A128370,
A128371,
A128372.
a(13), a(14), a(16), a(18), a(19), a(24), a(25), a(27), a(29), a(32) from
Alexander Adamchuk, Feb 17 2008
Corrected A-number in cross-reference. Copied a(8) to a(16) from other sequences. -
R. J. Mathar, Aug 08 2009
a(17) from Joe Crump (joecr(AT)carolina.rr.com), Sep 17 2009.
Showing 1-2 of 2 results.