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.

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A127820 a(n) = least k such that the remainder when 12^k is divided by k is n.

Original entry on oeis.org

11, 5, 15, 10, 7, 21, 25, 34, 549, 134, 120593747, 13, 20395, 26, 1713, 20, 203, 57, 49, 62, 1707, 122, 55, 30, 793, 118, 45, 58, 1921, 38, 1853, 56, 339, 110, 4223, 42, 85, 106, 1689, 52, 841, 642, 4475, 70, 51, 551, 11683, 147, 168061, 94, 129, 623, 1243895, 90
Offset: 1

Views

Author

Alexander Adamchuk, Jan 30 2007

Keywords

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127821.

Programs

  • Mathematica
    t = Table[0, {10000} ]; k = 1; While[ k < 3000000000, a = PowerMod[12, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 04 2009 *)

Extensions

More terms from Robert G. Wilson v, Feb 06 2007

A128154 a(n) = least k such that the remainder when 14^k is divided by k is n.

Original entry on oeis.org

13, 3, 11, 5, 33, 10, 1967, 9, 23587, 18, 2733, 46, 17651, 15, 93929, 20, 303, 178, 145, 22, 12901, 58, 2721, 25, 17990951, 27, 143, 36, 85, 166, 646123, 82, 2439143677, 55, 63, 76, 319, 123, 295, 52, 51, 77, 247380287953, 45, 5779134947, 90, 87, 74, 175, 146
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128155, A128156, A128157, A128158, A128159, A128160, A128149, A128150.

Programs

  • Mathematica
    t = Table[0, {10000} ]; k = 1; While[ k < 3000000000, a = PowerMod[14, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t
lk[n_]:=Module[{k=1},While[PowerMod[14,k,k]!=n,k++];k]; Array[lk,20] (* Harvey P. Dale, Aug 17 2013 *)

Extensions

More terms from Ryan Propper, Feb 28 2007
a(43) from Hagen von Eitzen, Aug 16 2009

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

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Examples

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

Links

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.

Programs

  • 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 *)

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

A128155 a(n) = least k such that the remainder when 15^k is divided by k is n.

Original entry on oeis.org

2, 13, 6, 11, 10, 533, 218, 119, 12, 145, 214, 57, 106, 17149, 17, 3736136819, 26, 117, 206, 143, 34, 427, 202, 871, 40, 25397, 54, 6877, 52, 115, 194, 6839309, 48, 4857103, 38, 63, 94, 94043, 62, 95, 46, 303, 182, 121214771, 55, 1137417899, 178, 3327, 116
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128156, A128157, A128158, A128159, A128160, A128149, A128150.

Programs

  • Mathematica
    t = Table[0, {10000} ]; k = 1; While[ k < 3000000000, a = PowerMod[15, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t

Extensions

More terms from Ryan Propper, Feb 28 2007

A128156 a(n) = least k such that the remainder when 16^k is divided by k is n.

Original entry on oeis.org

3, 7, 13, 6, 11, 10, 87, 62, 209, 18, 35, 122, 4083, 22, 16584420001, 17, 1343851, 34, 453, 44, 215, 26, 469, 58, 69, 46, 121, 36, 266461, 49, 813, 56, 19499, 74, 58501, 230, 123, 218, 2077, 78, 17845, 214, 579, 106, 24313642489, 90, 6541, 88, 57, 206
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128157, A128158, A128159, A128160, A128149, A128150.

Programs

  • Mathematica
    t = Table[0, {10000} ]; k = 1; While[ k < 4100000000, a = PowerMod[16, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t

Extensions

More terms from Ryan Propper, Feb 27 2007

A128157 a(n) = least k such that the remainder when 17^k is divided by k is n.

Original entry on oeis.org

2, 3, 7, 13, 142, 11, 25, 9, 10, 299, 57, 203, 46, 69, 274, 613024059983, 19, 7099195, 30, 21, 134, 24065, 38, 133, 28, 27, 205, 155591, 33, 20452755522967, 49, 165, 35, 391, 99, 94271801, 198, 39, 70, 23353, 62, 2759, 55, 1623, 122, 22649, 665, 1591398755
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128158, A128159, A128160, A128149, A128150.

Programs

  • Mathematica
    t = Table[0, {10000} ]; k = 1; While[ k < 4500000000, a = PowerMod[17, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t

Extensions

More terms from Hagen von Eitzen, Jul 31 2009
a(338) = 7615772967 = 3 * 11 * 230780999 [From Daniel Morel, May 18 2010]
a(100) = 36706228199, a(154) = 10618746241, a(444) = 10700153359, a(616) = 7969009427, a(720) = 11004291191, a(984) = 11601377453 [From Daniel Morel, Jun 15 2010]
a(184) = 16808380397, a(508) = 34412778035 [From Daniel Morel, Nov 05 2010]

A128158 a(n) = least k such that the remainder when 18^k is divided by k is n.

Original entry on oeis.org

17, 14, 5, 7, 13, 106, 11, 158, 927, 314, 6767, 15, 724317787, 62, 21, 20, 407, 19, 319, 38, 39, 302, 150698261, 30, 1055599, 298, 129, 74
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Comments

10^15 < a(29) <= 3612834616189533302730621726282897865691021. - Max Alekseyev, Apr 14 2012

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128159, A128160, A128149, A128150.

Programs

  • Mathematica
    t = Table[0, {10000}]; k = 1; While[k < 3000000000, a = PowerMod[18, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Jun 23 2009 *)

Extensions

a(13)-a(28) from Robert G. Wilson v, Jun 23 2009

A128159 a(n) = least k such that the remainder when 19^k is divided by k is n.

Original entry on oeis.org

2, 17, 358, 5, 7, 13, 118, 11, 22, 207, 14, 6683, 21, 1055, 221, 6843, 86, 39959, 23, 559, 34, 129, 26, 25, 51, 799, 334, 33, 166, 47427581, 1537, 901, 68, 39, 326, 87169, 44, 161, 46, 3509, 341, 529, 106, 1098179, 158, 657, 314, 49621349, 75, 143, 62, 749, 116
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Comments

a(447) = 7987803178, a(660) = 11147676413, a(923) = 6246715274. - Daniel Morel, Jun 08 2010
a(216) = 21686254249, a(296) = 40778012377, a(386) = 15891209603, a(582) = 46530896443, a(638) = 15297472657, a(736) = 45211411479, a(872) = 106458212591. - Daniel Morel, Oct 15 2010

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128160.
Cf. A128149, A128150.

Programs

Extensions

More terms from Ryan Propper, Mar 24 2007
More terms from Robert G. Wilson v, Aug 04 2009

A128160 a(n) = least k such that the remainder when 20^k is divided by k is n.

Original entry on oeis.org

19, 3, 17, 6, 15, 7, 13, 9, 11, 18, 7989, 92, 973, 33, 611, 24, 2661, 382, 559, 21, 96641237093, 42, 1887, 94, 155, 27, 60403, 36, 7971, 74, 1172954777, 46, 2470227509, 122, 45, 116, 1837, 362, 779, 60, 469, 358, 1275143, 51, 55, 118, 723, 49
Offset: 1

Views

Author

Alexander Adamchuk, Feb 16 2007

Keywords

Links

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821, A128154, A128155, A128156, A128157, A128158, A128159.
Cf. A128149, A128150.

Programs

  • Mathematica
    t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[20, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* Robert G. Wilson v, Aug 04 2009 *)

Extensions

More terms copied from a-file by Hagen von Eitzen, Oct 22 2009

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
Previous Showing 11-20 of 45 results. Next

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