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.

Showing 1-5 of 5 results.

A083529 a(n) = 5^n mod 3*n.

Original entry on oeis.org

2, 1, 8, 1, 5, 1, 5, 1, 26, 25, 5, 1, 5, 25, 35, 1, 5, 1, 5, 25, 62, 25, 5, 1, 50, 25, 80, 37, 5, 55, 5, 1, 26, 25, 80, 1, 5, 25, 8, 25, 5, 1, 5, 97, 80, 25, 5, 1, 68, 25, 125, 1, 5, 1, 155, 25, 125, 25, 5, 145, 5, 25, 188, 1, 5, 181, 5, 13, 125, 205, 5, 1, 5, 25, 125, 169, 80, 181, 5
Offset: 1

Views

Author

Labos Elemer, Apr 30 2003

Keywords

Comments

From Robert Israel, Dec 25 2014: (Start)
a(n) == (-1)^n mod 3.
a(n) = 1 if and only if n is even and in A067946.
For n > 3, a(n) = 5 if and only if n is odd and in A123091. (End)

Examples

			a(3) = 8 because 5^3 = 125 and 125 mod (3 * 3) = 8.
a(4) = 1 because 5^4 = 625 and 625 mod (3 * 4) = 1.

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A082511, A083528, A083530, A067946, A123091.

Programs

A083530 a(n) = 7^n mod (2*n).

Original entry on oeis.org

1, 1, 1, 1, 7, 1, 7, 1, 1, 9, 7, 1, 7, 21, 13, 1, 7, 1, 7, 1, 7, 5, 7, 1, 7, 49, 1, 49, 7, 49, 7, 1, 13, 49, 63, 1, 7, 49, 31, 1, 7, 49, 7, 25, 37, 49, 7, 1, 49, 49, 37, 9, 7, 1, 43, 49, 1, 49, 7, 1, 7, 49, 91, 1, 37, 37, 7, 89, 67, 49, 7, 1, 7, 49, 43, 121, 105, 25, 7, 1, 1, 49, 7, 49, 147, 49
Offset: 1

Views

Author

Labos Elemer, Apr 30 2003

Keywords

Examples

			For n = 5, a(5) = 7 because 7^5 = 16807 = 1680*10 + 7, that is 7^5 == 7 (mod 2*5).

Links

Crossrefs

Cf. A000079, A000244, A000351, A000420, A082511, A083528, A083529.

Programs

  • Mathematica
    Table[Mod[7^w, 2*w], {w, 1, 100}]
  • PARI
    a(n)=lift(Mod(7,2*n)^n) \\ Charles R Greathouse IV, Oct 03 2016

A082511 a(n) = 3^n mod 2n.

Original entry on oeis.org

1, 1, 3, 1, 3, 9, 3, 1, 9, 9, 3, 9, 3, 9, 27, 1, 3, 9, 3, 1, 27, 9, 3, 33, 43, 9, 27, 25, 3, 9, 3, 1, 27, 9, 47, 9, 3, 9, 27, 1, 3, 57, 3, 81, 63, 9, 3, 33, 31, 49, 27, 81, 3, 81, 67, 65, 27, 9, 3, 81, 3, 9, 27, 1, 113, 69, 3, 81, 27, 109, 3, 81, 3, 9, 57, 81, 75, 105, 3, 1, 81, 9, 3, 57, 73
Offset: 1

Views

Author

Labos Elemer, Apr 28 2003

Keywords

Examples

			Residues are often also powers of 3, that is, 3^n = k*2*n + 3^j, as is the case for n=1..23. The first terms that are not powers of 3 are a(24)=33 and a(25)=43.
a(6)=9: modulus = 2*n = 12; 3^n = 3^6 = 729 = 60*12 + 9 = 720 + a(6).

Links

Crossrefs

Cf. A000079, A000244, A002379.
Cf. A083528, A083529, A083530.

Programs

  • Mathematica
    Table[PowerMod[3,n,2n],{n,90}] (* Harvey P. Dale, Jan 21 2014 *)
  • PARI
    a(n) = lift(Mod(3, 2*n)^n) \\ Felix Fröhlich, Oct 20 2018
  • Python
    for n in range(1, 80): print(pow(3, n, 2*n), end=" ") # Stefano Spezia, Oct 20 2018

A191561 a(n) = 2^n mod 3*n.

Original entry on oeis.org

2, 4, 8, 4, 2, 10, 2, 16, 26, 4, 2, 28, 2, 4, 8, 16, 2, 28, 2, 16, 8, 4, 2, 64, 32, 4, 80, 16, 2, 64, 2, 64, 8, 4, 53, 28, 2, 4, 8, 16, 2, 64, 2, 16, 107, 4, 2, 64, 128, 124, 8, 16, 2, 82, 98, 88, 8, 4, 2, 136, 2, 4, 134, 64, 32, 64, 2, 16, 8, 184, 2, 136, 2, 4
Offset: 1

Views

Author

Vincenzo Librandi, Jul 31 2011

Keywords

Links

Crossrefs

Cf. A083528, A083529, A083530.

Programs

A191562 a(n) = 7^n mod 3*n.

Original entry on oeis.org

1, 1, 1, 1, 7, 1, 7, 1, 1, 19, 7, 1, 7, 7, 28, 1, 7, 1, 7, 1, 28, 49, 7, 1, 7, 49, 1, 49, 7, 19, 7, 1, 46, 49, 28, 1, 7, 49, 109, 1, 7, 91, 7, 25, 82, 49, 7, 1, 49, 49, 37, 61, 7, 1, 43, 49, 1, 49, 7, 1, 7, 49, 28, 1, 37, 37, 7, 157, 136, 49, 7, 1, 7, 49
Offset: 1

Views

Author

Vincenzo Librandi, Jul 31 2011

Keywords

Links

Crossrefs

Cf. A083528, A083529, A083530.

Programs

Showing 1-5 of 5 results.

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