A128172 -id:A128172 - cp's OEIS frontend

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

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Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found [Superseded by Cariboni table]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 *)

A128370 a(n) = least k such that the remainder of 30^k divided by k is n.

Original entry on oeis.org

29, 7, 26997, 13, 8471, 33, 23, 11, 721, 55, 19, 39, 17, 886, 21, 26, 803, 98, 13289, 22, 51, 878, 1141, 146, 35, 38, 111, 218, 515267673651961, 31, 3212679202339, 56, 267, 866, 4367, 42, 10129, 862, 57, 86, 42691, 13479, 949, 214, 95, 77, 7633, 52, 1469, 170, 429, 68, 2791229, 94, 215, 422, 3849, 842, 9773, 140

Offset: 1

Alexander Adamchuk, Feb 27 2007

nonn

Robert G. Wilson v 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, A128363, A128364, A128365, A128366, A128367, A128368, A129369, 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 < 5100000000, a = PowerMod[30, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 06 2009 *)

Terms a(29) onward from Max Alekseyev, Mar 22 2012

A126762 a(n) is the least k > n such that the remainder when n^k is divided by k is n.

Original entry on oeis.org

2, 3, 5, 5, 7, 7, 11, 9, 11, 11, 13, 13, 17, 15, 17, 17, 19, 19, 23, 21, 23, 23, 29, 25, 28, 27, 29, 29, 31, 31, 37, 33, 37, 35, 37, 37, 41, 39, 41, 41, 43, 43, 47, 45, 47, 47, 53, 49, 53, 51, 53, 53, 59, 55, 59, 57, 59, 59, 61, 61, 67, 63, 67, 65, 67, 67, 71, 69, 71, 71, 73, 73

Offset: 1

Alexander Adamchuk, Feb 17 2007

nonn

a(n-1) = n for n = {2,3,5,7,9,11,13,15,17,19,21,23,25,27,29,...} = 2 together with odd numbers n > 1.
a(n) coincides with A082048(n) up to n = 24.
a(n) is the smallest number k > n such that n^k == n (mod k). Conjecture: a(n) is the smallest number k > n such that n^(k-1) == 1 (mod k). Thus a(n) is coprime to n. - Thomas Ordowski, Aug 03 2018

Harvey P. Dale, Table of n, a(n) for n = 1..996

Cf. A128149 = Least k such that n^k (mod k) = n-1. Cf. A128172 = Least k such that n^k (mod k) = n+1. Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159, A128160. Cf. A082048 = least number greater than n having greater smallest prime factor than that of n.

Table[Min[Select[Range[101],PowerMod[n,#,# ]==n&]],{n,1,100}]
lkgn[n_]:=Module[{k=1},While[PowerMod[n,k,k]!=n,k++];k]; Array[lkgn,80] (* Harvey P. Dale, May 25 2021 *)

Name clarified by Thomas Ordowski, Aug 03 2018

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

Alexander Adamchuk, May 10 2010

nonn

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.

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 *)

A321365 Positive integers n such that 13^n == 14 (mod n).

Original entry on oeis.org

1, 5805311, 392908759, 399614833907, 2674764845549, 21997277871211, 67146783889057

Offset: 1

Max Alekseyev, Nov 08 2018

No other terms below 10^15.

Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), A116611 (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A321364 (k=12), this sequence (k=14), A116639 (k=15).

Cf. A116609, A127821, A128149, A128172.

is(n) = Mod(13, n)^n==14; \\ Felix Fröhlich, Nov 08 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

Alexander Adamchuk, May 10 2010

nonn

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.

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 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A128370 a(n) = least k such that the remainder of 30^k divided by k is n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A126762 a(n) is the least k > n such that the remainder when n^k is divided by k is n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A321365 Positive integers n such that 13^n == 14 (mod n).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica