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.

Previous Showing 11-20 of 20 results.

A116638 Positive integers n such that 13^n == 11 (mod n).

Original entry on oeis.org

1, 2, 158, 301823, 1851103, 8616098, 60528467, 1087582634, 1628818307, 16205558969
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Nov 07 2018
Large terms: 38763675625170712166, 527929122195463909516681113715859203.

Crossrefs

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), this sequence (k=11), A116639 (k=15).
Cf. A116609.

Programs

  • Mathematica
    Join[{1, 2}, Select[Range[1, 9000], Mod[13^#, #] == 11 &]] (* G. C. Greubel, Nov 20 2017 *)
Join[{1, 2}, Select[Range[10000000], PowerMod[13, #, #] == 11 &]] (* Robert Price, Apr 10 2020 *)

Extensions

More terms from Ryan Propper, Jan 11 2008
Edited by Max Alekseyev, May 04 2010

A116639 Numbers n such that 13^n == 15 (mod n).

Original entry on oeis.org

1, 2, 14, 22, 1582, 11266, 52766, 76202, 100562, 494371, 641141, 1698494, 66593158, 469296521, 10917186079, 12062558662, 4928050067287, 5315948729617, 29841213777637, 113215787397262, 778590786358582, 787324867879046
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. Some large terms: 6991413003775539262, 2360895769139218729155198091. - Max Alekseyev, Oct 15 2016

Crossrefs

Cf. A116609, A116611, A116620, A116621, A116622, A116629, A116630, A116631, A116632, A116636, A116638.

Programs

  • Mathematica
    Select[Range[25000000],PowerMod[13,#,# ]==15&] (* Harvey P. Dale, Feb 03 2009 *)

Extensions

One more term from Harvey P. Dale, Feb 03 2009
Edited by Max Alekseyev, Sep 19 2009
a(14)-a(22) from Max Alekseyev, May 04 2010, Apr 29 2014, Oct 15 2016

A295532 Positive integers n such that 13^n == 8 (mod n).

Original entry on oeis.org

1, 5, 371285, 3957661, 70348567451, 42831939409247
Offset: 1

Views

Author

Max Alekseyev, Nov 23 2017

Keywords

Comments

No other terms below 10^15.

Crossrefs

Cf. A116609, A127821, A015922, A277630.
Sequences 13^n == k (mod n): A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), A116611 (k=5), A116631 (k=6), A116632 (k=7), this sequence (k=8), A116636 (k=9), A116620 (k=10), A116638 (k=11), A116639 (k=15).

Programs

  • Mathematica
    Join[{1, 5}, Select[Range[4000000], PowerMod[13, #, #] == 8 &]] (* Robert Price, Apr 10 2020 *)

A056969 a(n) = 10^n modulo n.

Original entry on oeis.org

0, 0, 1, 0, 0, 4, 3, 0, 1, 0, 10, 4, 10, 2, 10, 0, 10, 10, 10, 0, 13, 12, 10, 16, 0, 22, 1, 4, 10, 10, 10, 0, 10, 32, 5, 28, 10, 24, 25, 0, 10, 22, 10, 12, 10, 8, 10, 16, 31, 0, 31, 16, 10, 28, 10, 16, 31, 42, 10, 40, 10, 38, 55, 0, 30, 34, 10, 4, 34, 60, 10, 64, 10, 26, 25, 44, 54, 40
Offset: 1

Views

Author

Henry Bottomley, Jul 20 2000

Keywords

Examples

			a(7) = 3 since 10000000 = 7*1428571+3

Links

Crossrefs

Cf. k^n mod n: A015910 (k=2), A066601 (k=3), A066602 (k=4), A066603 (k=5), A066604 (k=6), A066438 (k=7), A066439 (k=8), A066440 (k=9), this sequence (k=10), A066441 (k=11), A066442 (k=12), A116609 (k=13).

Programs

  • Maple
    seq(irem(10^n,n),n=1..78); # Zerinvary Lajos, Apr 20 2008
  • Mathematica
    Table[PowerMod[10, n, n], {n, 80} ]
  • PARI
    a(n) = lift(Mod(10, n)^n); \\ Michel Marcus, Oct 19 2017

Formula

a(n) = 10*A056968(n) mod n = A011557(n) mod n.

A066438 a(n) = 7^n mod n.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 0, 1, 1, 9, 7, 1, 7, 7, 13, 1, 7, 1, 7, 1, 7, 5, 7, 1, 7, 23, 1, 21, 7, 19, 7, 1, 13, 15, 28, 1, 7, 11, 31, 1, 7, 7, 7, 25, 37, 3, 7, 1, 0, 49, 37, 9, 7, 1, 43, 49, 1, 49, 7, 1, 7, 49, 28, 1, 37, 37, 7, 21, 67, 49, 7, 1, 7, 49, 43, 45, 28, 25, 7, 1
Offset: 1

Views

Author

Robert G. Wilson v, Dec 27 2001

Keywords

Links

Crossrefs

Cf. k^n mod n; A015910 (k=2), A066601 (k=3), A066602 (k=4), A066603 (k=5), A066604 (k=6), this sequence (k=7), A066439 (k=8), A066440 (k=9), A056969 (k=10), A066441 (k=11), A066442 (k=12), A116609 (k=13).

Programs

  • Maple
    seq(irem(7^n,n),n=1..80); # Zerinvary Lajos, Apr 20 2008
  • Mathematica
    Table[PowerMod[7, n, n], {n, 80} ]
  • PARI
    a(n) = { lift(Mod(7, n)^n) } \\ Harry J. Smith, Feb 14 2010

A066603 a(n) = 5^n mod n.

Original entry on oeis.org

0, 1, 2, 1, 0, 1, 5, 1, 8, 5, 5, 1, 5, 11, 5, 1, 5, 1, 5, 5, 20, 3, 5, 1, 0, 25, 26, 9, 5, 25, 5, 1, 26, 25, 10, 1, 5, 25, 8, 25, 5, 1, 5, 9, 35, 25, 5, 1, 19, 25, 23, 1, 5, 1, 45, 25, 11, 25, 5, 25, 5, 25, 62, 1, 5, 49, 5, 13, 56, 65, 5, 1, 5, 25, 50, 17, 3, 25, 5, 65, 80, 25, 5, 1, 65
Offset: 1

Views

Author

Amarnath Murthy, Dec 22 2001

Keywords

Examples

			a(7) = 5 as 5^7 = 78125 = 7*11160 + 5.

Links

Crossrefs

Cf. k^n mod n: A015910 (k=2), A066601 (k=3), A066602 (k=4), this sequence (k=5), A066604 (k=6), A066438 (k=7), A066439 (k=8), A066440 (k=9), A056969 (k=10), A066441 (k=11), A066442 (k=12), A116609 (k=13).

Programs

  • Maple
    seq(irem(5^n,n),n=1..85); # Zerinvary Lajos, Apr 20 2008
  • Mathematica
    Table[PowerMod[5, n, n], {n, 85} ]
  • PARI
    a(n) = { lift(Mod(5, n)^n) } \\ Harry J. Smith, Mar 09 2010

Extensions

More terms from Robert G. Wilson v, Dec 27 2001

A066441 a(n) = 11^n mod n.

Original entry on oeis.org

0, 1, 2, 1, 1, 1, 4, 1, 8, 1, 0, 1, 11, 9, 11, 1, 11, 1, 11, 1, 8, 11, 11, 1, 1, 17, 26, 25, 11, 1, 11, 1, 11, 19, 16, 1, 11, 7, 5, 1, 11, 1, 11, 33, 26, 29, 11, 1, 18, 1, 5, 29, 11, 1, 11, 9, 20, 5, 11, 1, 11, 59, 8, 1, 46, 55, 11, 21, 20, 11, 11, 1, 11, 47, 26, 49, 44, 25, 11, 1
Offset: 1

Views

Author

Robert G. Wilson v, Dec 27 2001

Keywords

Links

Crossrefs

Cf. k^n mod n: A015910 (k=2), A066601 (k=3), A066602 (k=4), A066603 (k=5), A066604 (k=6), A066438 (k=7), A066439 (k=8), A066440 (k=9), A056969 (k=10), this sequence (k=11), A066442 (k=12), A116609 (k=13).

Programs

  • Maple
    seq(irem(11^n,n),n=1..80); # Zerinvary Lajos, Apr 20 2008
  • Mathematica
    Table[PowerMod[11, n, n], {n, 80} ]
  • PARI
    a(n) = { lift(Mod(11, n)^n) } \\ Harry J. Smith, Feb 14 2010

A114448 Array a(n,k) = n^k (mod k) read by antidiagonals (k>=1, n>=1).

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 3, 4, 1, 0, 1, 0, 1, 4, 3, 2, 1, 0, 0, 1, 0, 0, 4, 3, 0, 1, 0, 1, 2, 1, 1, 1, 4, 1, 8, 1, 0, 0, 0, 0, 2, 0, 5, 0, 0, 4, 1, 0, 1, 1, 1, 3, 1, 6, 1, 1, 9, 2, 1, 0, 0, 2, 0, 4, 4, 0, 0, 8, 6, 3, 4, 1, 0, 1, 0, 1, 0, 3, 1, 1, 0, 5, 4, 9, 2, 1
Offset: 1

Views

Author

Leroy Quet, Feb 14 2006

Keywords

Comments

Alternate description: triangular array a(n, k) = n^k (mod k) read by rows (n > 1, 0 < k < n). This is equivalent because a(n, k) = a(n-k, k). - David Wasserman, Jan 25 2007

Examples

			2^6 = 64 and 64 (mod 6) is 4. So a(2,6) = 4.

Crossrefs

Cf. A051127, A051128, A094263. Transpose of A060154. First 13 rows are A057427(n-1), A015910, A066601, A066602, A066603, A066604, A066438, A066439, A066440, A056969, A066441, A066442, A116609. First 12 columns are A000004, A000035, A010872, A000035, A010874, A070431, A010876, A000035, A021559(n+1), A008959, A010880, A070435.

Programs

  • Mathematica
    a[n_, k_] := Mod[n^k, k]; Table[a[n - k + 1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 12 2012 *)

Extensions

More terms from David Wasserman, Jan 25 2007

A321364 Positive integers m such that 13^m == 12 (mod m).

Original entry on oeis.org

1, 13757837, 6969969233, 514208575135
Offset: 1

Views

Author

Max Alekseyev, Nov 07 2018

Keywords

Comments

No other terms below 10^15.
Some larger terms: 14551705803598782884189, 268766423508299769671017810348321281664525668552158231.

Crossrefs

Solutions to 13^m == k (mod m): 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), this sequence (k=12), A321365 (k=14), A116639 (k=15).
Cf. A116609, A127821, A128149.

Programs

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

Views

Author

Max Alekseyev, Nov 08 2018

Keywords

Comments

No other terms below 10^15.

Crossrefs

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.

Programs

Previous Showing 11-20 of 20 results.

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