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 1-4 of 4 results.

A188948 Values of x such that x^2 + y^2 = 13^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

0, 2, 5, 9, 119, 122, 828, 4449, 239, 56403, 145668, 246046, 3369960, 3627003, 23161315, 128629846, 13651680, 1590277918, 4241902555, 6712571031, 95420159401, 107655263398, 647549275812, 3718150825791, 584824319281, 44827014819597, 123471611274972, 182714776311554, 2701419604443960, 3190610873034597, 18094618450123325
Offset: 0

Views

Author

Zak Seidov, Apr 10 2011

Keywords

Comments

The y values are in A188949.

Crossrefs

Programs

  • Mathematica
    Table[Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &][[1,1]], {n, 0, 30}]

Extensions

Edited by T. D. Noe, Apr 14 2011

A188949 Values of y such that x^2 + y^2 = 13^n with x and y coprime and 0 < x < y.

Original entry on oeis.org

1, 3, 12, 46, 120, 597, 2035, 6554, 28560, 86158, 341525, 1315911, 3455641, 17021162, 58317492, 186118929, 815616479, 2474152797, 9719139348, 37641223154, 99498527400, 485257533003, 1671083125805, 5284814079046, 23290743888720, 71041880304722, 276564805068235
Offset: 0

Views

Author

Zak Seidov, Apr 10 2011

Keywords

Comments

The x values are in A188948.

Crossrefs

Programs

  • Mathematica
    Table[Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &][[1,2]], {n, 0, 30}]

Extensions

Edited by T. D. Noe, Apr 14 2011

A188982 Even numbers x such that x^2 + y^2 = 13^n with x and y coprime.

Original entry on oeis.org

0, 2, 12, 46, 120, 122, 828, 6554, 28560, 86158, 145668, 246046, 3369960, 17021162, 58317492, 128629846, 13651680, 1590277918, 9719139348, 37641223154, 99498527400, 107655263398, 647549275812, 5284814079046, 23290743888720, 71041880304722, 123471611274972, 182714776311554, 2701419604443960, 13833225534613558, 47880898349909868
Offset: 0

Views

Author

T. D. Noe, Apr 14 2011

Keywords

Comments

The y values are in A188983.
This is also the absolute value of the imaginary part of (3+2i)^n, where i = sqrt(-1).

Crossrefs

Programs

  • Magma
    [Integers()!Abs(Im((3+2*Sqrt(-1))^n)): n in [0..30]]; // Bruno Berselli, May 26 2011
  • Mathematica
    Table[s = Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &, 1][[1]]; Select[s, EvenQ][[1]], {n, 0, 30}]

A188983 Odd numbers y such that x^2 + y^2 = 13^n with x and y coprime.

Original entry on oeis.org

1, 3, 5, 9, 119, 597, 2035, 4449, 239, 56403, 341525, 1315911, 3455641, 3627003, 23161315, 186118929, 815616479, 2474152797, 4241902555, 6712571031, 95420159401, 485257533003, 1671083125805, 3718150825791, 584824319281, 44827014819597, 276564805068235, 1076637637754649, 2864483360640839, 3190610873034597, 18094618450123325
Offset: 0

Views

Author

T. D. Noe, Apr 14 2011

Keywords

Comments

The x values are in A188982.
This is also the absolute value of the real part of (3+2i)^n, where i = sqrt(-1). The signed version is A121622.

Crossrefs

Programs

  • Magma
    [Integers()!Abs(Real((3+2*Sqrt(-1))^n)): n in [0..30]]; // Bruno Berselli, May 26 2011
  • Mathematica
    Table[s = Select[PowersRepresentations[13^n, 2, 2], CoprimeQ @@ # &, 1][[1]]; Select[s, OddQ][[1]], {n, 0, 30}]
Showing 1-4 of 4 results.