A128149 -id:A128149 - cp's OEIS frontend

A128361 a(n) = least k such that the remainder when 21^k is divided by k is n.

2, 19, 6, 17, 218, 15, 14, 13, 12, 11, 86, 9249, 214, 133, 69, 4084085, 106, 39, 422, 581831, 23, 5053, 38, 9237, 26, 775, 46, 1253, 206, 51, 82, 671, 34, 617741981, 58, 45, 202, 289, 87, 6401, 185, 217, 341, 3485351, 66, 2718013, 394, 111, 56, 8064317, 75

Offset: 1

Alexander Adamchuk, Feb 27 2007

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

Cf. A128362, A128363, A128364, A128365, A128366, A128367, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000}]; k = 1; While[k < 3000000000, a = PowerMod[21, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k]; k++ ]; t (* Robert G. Wilson v, Jun 25 2009 *)
lk[n_]:=Module[{k=1},While[PowerMod[21,k,k]!=n,k++];k]; Array[lk,60] (* The program takes a long time to run *) (* Harvey P. Dale, Oct 22 2016 *)

a(16) - a(51) from Robert G. Wilson v, Jun 25 2009

A128362 a(n) = least k such that the remainder when 22^k is divided by k is n.

Original entry on oeis.org

3, 5, 19, 6, 17, 478, 25, 14, 13, 18, 187, 118, 15, 94, 1032913, 20, 64311245, 466, 3543, 58, 305197, 23, 1535, 46, 10623, 458, 5099785, 36, 2723, 454, 10617, 226, 55, 87, 35459, 140, 45, 446, 1373093, 51, 3604637279, 65, 75, 110, 23299, 57, 305, 52, 10599

Offset: 1

Alexander Adamchuk, Feb 27 2007

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

Cf. A128361, A128363, A128364, A128365, A128366, A128367, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000}]; k = 1; While[k < 4000000000, a = PowerMod[22, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Jun 26 2009 *)

a(15) - a(40) from Robert G. Wilson v, Jun 26 2009

a(41) - a(49) from Robert G. Wilson v, Jun 27 2009

A128363 a(n) = least k such that the remainder when 23^k is divided by k is n.

Original entry on oeis.org

2, 3, 5, 19, 262, 17, 58, 9, 10, 13, 14, 55, 86, 12153, 514, 111823, 95, 25, 30, 12147, 68, 235, 29, 280517, 56, 27, 502, 16805, 51, 49, 166, 35, 62, 1837, 38, 977969, 82, 39, 1370, 289, 122, 9822698929535, 65, 133, 697, 161, 303, 19445, 50, 147, 259, 1247

Offset: 1

Alexander Adamchuk, Feb 27 2007

Max Alekseyev et al., Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found

Cf. A128361, A128362, A128364, A128365, A128366, A128367, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[23, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 04 2009 *)
Table[Module[{k=1},While[PowerMod[23,k,k]!=n,k++];k],{n,35}] (* The program generates the first 35 terms of the sequence. *) (* Harvey P. Dale, Jul 18 2025 *)

a(42), a(64) from Hagen von Eitzen, Aug 04 2009
a(750), a(770), a(234), a(274), a(406), a(600), a(610), a(754) from Daniel Morel, May 31, Aug 24, Sep 20 2010
a(84) from Max Alekseyev, Apr 13 2012

A128364 a(n) = least k such that the remainder when 24^k is divided by k is n.

Original entry on oeis.org

23, 11, 7, 5, 19, 10, 17, 142, 15, 566, 13, 78, 5865637, 205, 13809, 20, 589, 39, 35, 278, 129, 554, 459207143, 25, 148731221, 50, 63, 274, 2855, 33, 49, 34, 5429, 542, 5528521301, 42, 2773, 538, 185, 77, 3220589, 66, 90553, 956, 2317, 70, 161, 104

Offset: 1

Alexander Adamchuk, Feb 27 2007

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

Cf. A128361, A128362, A128363, A128365, A128366, A128367, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000}]; k = 1; While[k < 3600000000, a = PowerMod[25, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Jun 29 2009 *)
lk[n_] := Module[{k = 1}, While[PowerMod[24, k, k] != n, k++]; k]; Array[ lk,48] (* Harvey P. Dale, Jan 18 2019 *)

a(13) - a(34) from Robert G. Wilson v, Jun 29 2009

A128365 a(n) = least k such that the remainder when 25^k is divided by k is n.

Original entry on oeis.org

2, 23, 11, 7, 10, 19, 57, 17, 14, 15, 614, 13, 34

Offset: 1

Alexander Adamchuk, Feb 27 2007

a(14) > 10^15. - Max Alekseyev, Apr 14 2012

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
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, Oct 30 2016 [With 182 new terms, this supersedes the earlier table from Robert G. Wilson v]

Cf. A128361, A128362, A128363, A128364, A128366, A128367, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[25, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 04 2009 *)

A128366 a(n) = least k such that the remainder when 26^k is divided by k is n.

Original entry on oeis.org

5, 3, 23, 6, 7, 10, 19, 9, 17, 18, 15, 92, 18881, 319, 36091, 20, 203, 94, 49, 21, 42395, 42, 17553, 326, 106709, 27, 2062919, 36, 14099, 34, 35, 46, 850984699, 214, 5847, 44, 341, 58, 377, 106, 105, 634, 301265879, 158, 93107, 90, 759, 176, 187, 69, 685, 78

Offset: 1

Alexander Adamchuk, Feb 27 2007

If a(199) exists, a(199) >= 148000000000. - Zhuorui He, Jul 24 2025

Zhuorui He, Table of n, a(n) for n = 1..198 (first 152 terms from Robert G. Wilson v).
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

Cf. A128361, A128362, A128363, A128364, A128365, A128367, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000}]; k = 1; lst = {}; While[k < 1200000000, a = PowerMod[26, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]; If[a + 1 == k, AppendTo[lst, a]; Print@lst]]; k++ ]; lst (* Robert G. Wilson v, Jun 30 2009 *)

a(27)-a(52) from Robert G. Wilson v, Jun 30 2009

A128367 a(n) = least k such that the remainder when 27^k is divided by k is n.

Original entry on oeis.org

2, 5, 6, 23, 11, 7, 25, 19, 10, 17, 718, 165, 35, 533, 33, 3738251, 178, 57, 142, 9779, 60, 2227273193, 55, 19659, 724, 17678421233, 29, 17473, 70, 19653, 209, 3005, 48, 28777, 694, 111, 346, 1441, 46, 15977, 86, 3399, 12614, 4387, 116, 527

Offset: 1

Alexander Adamchuk, Feb 27 2007

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

Cf. A128361, A128362, A128363, A128364, A128365, A128366, A128368, A128369, A129370, A128371, 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.

t = Table[0, {10000} ]; k = 1; While[ k < 4500000000, a = PowerMod[27, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 06 2009 *)

a(16) - a(25) from Robert G. Wilson v, Aug 06 2009

A128368 a(n) = least k such that the remainder when 28^k is divided by k is n.

Original entry on oeis.org

3, 13, 5, 6, 23, 11, 15, 194, 19, 18, 17, 148, 213, 22, 131209, 20, 2335, 25, 7311, 44, 259, 51, 5263, 38, 21927, 758, 240055, 29, 803, 58, 21921, 55, 4405, 39, 413, 316, 549, 746, 17831, 62, 4367, 106, 165, 74, 19253, 82, 6455, 88, 147, 734, 62093, 122

Offset: 1

Alexander Adamchuk, Feb 27 2007

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

Cf. A128361, A128362, A128363, A128364, A128365, A128366, A128367, A128369, A129370, A128371, 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.

t = Table[0, {10000} ]; k = 1; While[ k < 5000000000, a = PowerMod[28, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 06 2009 *)

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

Alexander Adamchuk, Feb 27 2007

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.]

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.

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 *)

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

A128369 a(n) = least k such that the remainder when 29^k is divided by k is n.

Original entry on oeis.org

2, 3, 13, 5, 22, 23, 11, 9, 26, 19, 51, 17, 46, 15, 118, 178523, 152, 92634008921, 102, 24369, 82, 2873, 93, 25, 34, 27, 74, 11227, 31, 39259, 830, 69, 136, 817, 62, 2429, 66, 24351, 802, 121, 184, 3405997613, 714, 45, 398, 5846879, 794, 221, 114

Offset: 1

Alexander Adamchuk, Feb 27 2007

a(408) = 9848641373 = 60343 * 163211.
a(756) = 10012502599 = 11 * 19 * 47906711.
a(886) = 12256265747, a(966) = 10085567837. - Daniel Morel, Jun 08 2010
a(378) = 31113438371, a(492) = 18377996647, a(730) = 22778710711. - Daniel Morel, Jul 05 2010
a(802) = 20290196677, a(826) = 21466370573. - Daniel Morel, Aug 24 2010

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

Cf. A128361, A128362, A128363, A128364, A128365, A128366, A128367, A128368, A129370, A128371, 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.

t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[29, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 06 2009 *)

cp's OEIS Frontend

A128361 a(n) = least k such that the remainder when 21^k is divided by k is n.

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A128362 a(n) = least k such that the remainder when 22^k is divided by k is n.

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A128363 a(n) = least k such that the remainder when 23^k is divided by k is n.

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A128364 a(n) = least k such that the remainder when 24^k is divided by k is n.

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A128365 a(n) = least k such that the remainder when 25^k is divided by k is n.

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A128366 a(n) = least k such that the remainder when 26^k is divided by k is n.

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A128367 a(n) = least k such that the remainder when 27^k is divided by k is n.

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Extensions

A128368 a(n) = least k such that the remainder when 28^k is divided by k is n.

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

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