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 11-15 of 15 results.

A054713 Number of powers of 13 modulo n.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 2, 2, 3, 4, 10, 1, 2, 2, 4, 4, 4, 3, 18, 4, 2, 10, 11, 2, 20, 2, 9, 2, 14, 4, 30, 8, 10, 4, 4, 3, 36, 18, 2, 4, 40, 2, 21, 10, 12, 11, 46, 4, 14, 20, 4, 2, 13, 9, 20, 2, 18, 14, 58, 4, 3, 30, 6, 16, 5, 10, 66, 4, 11, 4, 70, 6, 72, 36, 20, 18, 10, 2, 39, 4, 27, 40, 82, 2, 4
Offset: 1

Views

Author

Henry Bottomley, Apr 20 2000

Keywords

Links

Crossrefs

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054714 (14), A054715 (15), A054716 (16).

Programs

  • Mathematica
    a[n_] := Module[{e = IntegerExponent[n, 13]}, e + MultiplicativeOrder[13, n/13^e]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

A054714 Number of powers of 14 modulo n.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 2, 4, 6, 3, 5, 4, 1, 2, 2, 5, 16, 7, 18, 4, 3, 6, 22, 5, 10, 2, 18, 3, 28, 3, 15, 6, 10, 17, 3, 8, 12, 19, 2, 5, 8, 3, 21, 7, 6, 23, 23, 6, 3, 11, 16, 3, 52, 19, 10, 4, 18, 29, 58, 4, 6, 16, 7, 7, 2, 11, 11, 18, 22, 3, 10, 9, 72, 13, 10, 20, 6, 3, 26, 6, 54, 9, 82, 4, 16
Offset: 1

Views

Author

Henry Bottomley, Apr 20 2000

Keywords

Links

Crossrefs

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054715 (15), A054716 (16).

Programs

  • Mathematica
    a[n_] := Module[{e = IntegerExponent[n, {2, 7}]}, Max[e] + MultiplicativeOrder[14, n/Times @@ ({2, 7}^e)]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

A054715 Number of powers of 15 modulo n.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 1, 2, 3, 2, 5, 3, 12, 1, 2, 2, 8, 3, 18, 3, 2, 5, 22, 3, 3, 12, 4, 2, 28, 2, 10, 2, 6, 8, 2, 4, 36, 18, 13, 3, 40, 2, 21, 10, 3, 22, 46, 3, 7, 3, 9, 12, 13, 4, 6, 2, 19, 28, 29, 3, 15, 10, 3, 4, 13, 6, 11, 8, 23, 2, 35, 4, 72, 36, 3, 18, 5, 13, 26, 3, 5, 40, 82, 3, 9, 21, 29
Offset: 1

Views

Author

Henry Bottomley, Apr 20 2000

Keywords

Links

Crossrefs

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054716 (16).

Programs

  • Mathematica
    a[n_] := Module[{e = IntegerExponent[n, {3, 5}]}, Max[e] + MultiplicativeOrder[15, n/Times @@ ({3, 5}^e)]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

A054716 Number of powers of 16 modulo n.

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 5, 2, 3, 4, 1, 2, 2, 4, 9, 2, 3, 6, 11, 2, 5, 4, 9, 4, 7, 2, 5, 3, 5, 3, 3, 4, 9, 10, 3, 2, 5, 4, 7, 6, 3, 12, 23, 2, 21, 6, 2, 4, 13, 10, 5, 4, 9, 8, 29, 2, 15, 6, 3, 3, 3, 6, 33, 3, 11, 4, 35, 4, 9, 10, 5, 10, 15, 4, 39, 2, 27, 6, 41, 4, 2, 8, 7, 6, 11, 4, 3, 12, 5, 24
Offset: 1

Views

Author

Henry Bottomley, Apr 20 2000

Keywords

Links

Crossrefs

Cf. A054703 (base 2), A054704 (3), A054705 (4), A054706 (5), A054707 (6), A054708 (7), A054709 (8), A054717 (9), A054710 (10), A351524 (11), A054712 (12), A054713 (13), A054714 (14), A054715 (15).

Programs

  • Mathematica
    a[n_] := IntegerExponent[8*n, 16] + MultiplicativeOrder[16, n/2^IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Aug 25 2024 *)

A054711 Multiplicative order of 11 mod n, where gcd(n, 11) = 1.

Original entry on oeis.org

1, 1, 2, 2, 1, 2, 3, 2, 6, 1, 2, 12, 3, 2, 4, 16, 6, 3, 2, 6, 22, 2, 5, 12, 18, 6, 28, 2, 30, 8, 16, 3, 6, 6, 3, 12, 2, 40, 6, 7, 6, 22, 46, 4, 21, 5, 16, 12, 26, 18, 6, 6, 28, 58, 2, 4, 30, 6, 16, 12, 66, 16, 22, 3, 70, 6, 72, 6, 10, 6, 12, 39, 4, 54, 40, 41
Offset: 1

Views

Author

Henry Bottomley, Apr 20 2000

Keywords

Comments

The original version "Number of powers of 11 modulo n" that was similar to A054703-A054717 is now in A351524. - Georg Fischer, Feb 13 2022

Crossrefs

Cf. A053446 (of 3 mod n), A053448 (5), A053449 (6), A053450 (7), A053452 (9).
Cf. A351524.

Programs

  • Mathematica
    MultiplicativeOrder[11, #] & /@ Select[ Range@ 90, GCD[11, #] == 1 &] (* Robert G. Wilson v, Apr 05 2011 *)
  • PARI
    lista(nn) = {for(n=1, nn, if (gcd(n, 11) == 1, print1(znorder(Mod(11, n)), ", ")););} \\ Michel Marcus, Feb 09 2015

Extensions

Corrected by Michel Marcus, Feb 11 2015
Previous Showing 11-15 of 15 results.

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