cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A128372 a(n) = least k such that the remainder when 32^k is divided by k is n.

Original entry on oeis.org

31, 3, 29, 6, 201, 13, 25, 9, 23, 11, 183, 22, 19, 159, 17, 20, 45, 49, 169, 502, 209, 42, 35, 50, 91919, 27, 3265, 36, 1159, 98, 75197, 33, 95, 66, 2817, 38, 1385, 58, 25187, 82, 32727, 982, 55, 117, 7031, 91, 2517, 52, 46528545441593, 57, 503981, 92, 135, 194
Offset: 1

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Comments

Values a(50), ..., a(149) are relatively small again (starting 57, 503981, 92, 135, 194, 576353, 87, 125, 1902, 6019, 323, 43335727, 69, ...). - Hagen von Eitzen, Jun 04 2009

Links

Crossrefs

Cf. A128361, A128362, A128363, A128364, A128365, A128366, A128367, A128368, A129369, A128370, A128371. 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 < 4000000000, a = PowerMod[32, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 06 2009 *)

Extensions

Incorrect comment removed by Hagen von Eitzen, Jul 19 2009
a(49) found by Hagen von Eitzen, Jul 20 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

Views

Author

Alexander Adamchuk, Feb 16 2007, May 06 2007

Keywords

Examples

			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.

Crossrefs

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.

Extensions

More terms from Alexander Adamchuk, Dec 24 2007
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
Edited by Robert G. Wilson v, Aug 20 2009
a(17) from Joe Crump (joecr(AT)carolina.rr.com), Sep 17 2009.
More terms and general editing from Robert G. Wilson v, Sep 30 2009
a(20)-a(22) from Robert G. Wilson v, Oct 17 2009
a(23), a(30) from Max Alekseyev, Feb 11, Mar 31 2010

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

Original entry on oeis.org

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

Views

Author

Alexander Adamchuk, Feb 27 2007

Keywords

Links

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

A178194 Smallest k such that 33^k mod k = n.

Original entry on oeis.org

1, 2, 31, 5, 29, 7, 21, 13, 13684967, 10, 23, 14, 15, 538, 19, 42, 17, 35, 25, 49, 16861, 60, 55, 26, 1157, 38, 511, 54, 30197665, 106, 14691, 46, 155, 37, 18791, 62, 369, 164, 145, 93, 63517, 92, 115, 1046, 3113077, 58, 1376107, 1042, 105, 50, 221
Offset: 0

Views

Author

Artur Jasinski, May 22 2010

Keywords

Comments

smallest k such that m^k mod k = n
m=2 see A036236
m=3 see A078457
m=4 see A119678
m=5 see A119679
m=6 see A127816
m=7 see A119715
m=8 see A119714
m=9 see A127817
m=10 see A127818
m=11 see A127819
m=12 see A127820
m=13 see A127821
m=14 see A128154
m=15 see A128155
m=16 see A128156
m=17 see A128157
m=18 see A128158
m=19 see A128159
m=20 see A128160
m=21 see A128361
m=22 see A128362
m=23 see A128363
m=24 see A128364
m=25 see A128365
m=26 see A128366
m=27 see A128367
m=28 see A128368
m=29 see A128369
m=30 see A128370
m=31 see A128371
m=32 see A128372
m=33 see A178194
m=34 see A178195
m=35 see A178196
m=36 see A178197
m=37 see A178198
m=38 see A178199
m=39 see A178200
m=40 see A178201
m=41 see A178202

Crossrefs

see comment line.

Programs

  • Mathematica
    aa = {}; Do[k = 1; While[PowerMod[33, k, k] != n, k++ ]; Print[k]; AppendTo[aa, k], {n, 0, 50}]; aa

A177495 a(n) is the least k such that the remainder when 100^k is divided by k is n.

Original entry on oeis.org

3, 7, 97, 6, 19, 38, 31, 23, 13, 15, 89, 22, 29, 43, 17, 24, 83, 41, 19003, 580, 79, 42, 1903, 58, 35, 37, 73, 36, 71, 49, 999969, 56, 67, 66, 145, 76, 411, 578, 61, 60, 59, 494, 51, 262, 55, 158, 53, 52, 57, 398, 15673, 69, 1589, 9946, 65, 88, 20940211, 366, 391
Offset: 1

Views

Author

Alexander Adamchuk, May 10 2010

Keywords

Crossrefs

Cf. 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.
Cf. A128149, A128150, A128172.

Programs

  • Mathematica
    t = Table[0, {70}]; k = 1; While[k < 210000000, a = PowerMod[100, k, k]; If[a < 71 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t
Table[Module[{k=1},While[PowerMod[100,k,k]!=n,k++];k],{n,60}] (* Harvey P. Dale, Jun 06 2018 *)

A177496 a(n) is the least k such that the remainder when 1000^k is divided by k is n.

Original entry on oeis.org

3, 62, 997, 6, 115, 7, 51, 14, 991, 11, 23, 13, 21, 17, 197, 24, 983, 158, 109, 35, 89, 42, 977, 61, 39, 34, 139, 36, 971, 38, 3291, 188, 967, 66, 193, 92, 57, 74, 999161, 52, 137, 479, 69, 239, 191, 53, 953, 49, 317, 70, 73, 79, 947, 65291, 63, 59, 448991, 114, 941
Offset: 1

Views

Author

Alexander Adamchuk, May 10 2010

Keywords

Crossrefs

Cf. 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, A177495.
Cf. A128149, A128150, A128172.

Programs

  • Mathematica
    t = Table[0, {98}]; k = 1; While[k < 10000000, a = PowerMod[1000, k, k]; If[a < 99 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t
lk[n_]:=Module[{k=1},While[PowerMod[1000,k,k]!=n,k++];k]; Array[lk,60] (* Harvey P. Dale, Jul 21 2021 *)
Showing 1-6 of 6 results.

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