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.

A054875 Number of pairwise incongruent triangles with integer sides and positive integer area and longest side of length n.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 3, 1, 3, 1, 0, 3, 2, 0, 0, 3, 4, 4, 0, 1, 2, 7, 0, 1, 0, 3, 3, 2, 5, 0, 6, 7, 4, 4, 0, 2, 4, 0, 0, 5, 0, 6, 7, 10, 4, 1, 3, 4, 0, 4, 0, 10, 3, 0, 3, 1, 11, 3, 0, 8, 1, 5, 0, 4, 6, 7, 13, 0, 3, 9, 0, 10, 0, 6, 0
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Links

Crossrefs

Cf. A054876, A055592, A070787, A123323, A239246, A322105.

Programs

  • Mathematica
    okQ[x_, y_, z_] := If[x + y <= z, False, Module[{s = (x + y + z)/2}, IntegerQ[ Sqrt[s(s-x)(s-y)(s-z)]]] ]; a[n_] := Module[{num = 0}, Do[Do[If[okQ[x,y,n], num++], {x,1,y}], {y,1,n}]; num]; Array[a, 100] (* Amiram Eldar, Nov 22 2018 *)

Extensions

Name and offset changed to align with 2012 changes to A054876 by Peter Munn, Nov 23 2018

A070786 Area of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

Original entry on oeis.org

1, 1, 2, 2, 1, 3, 1, 2, 3, 4, 3, 2, 1, 3, 3, 6, 2, 4, 2, 4, 6, 1, 3, 5, 2, 4, 3, 6, 2, 3, 1, 5, 1, 4, 4, 2, 6, 7, 3, 6, 8, 6, 3, 1, 3, 5, 6, 4, 8, 2, 5, 10, 1, 4, 2, 6, 3, 7, 9, 5, 9, 7, 3, 2, 4, 1, 8, 9, 5, 7, 10, 3, 6, 9, 12, 4, 2, 8, 6, 4, 2, 10, 8, 12, 6, 2, 6, 3, 1, 7, 5, 10, 11, 4, 8, 7, 14, 3, 6, 3
Offset: 1

Views

Author

Henry Bottomley, May 07 2002

Keywords

Examples

			a(6)=3 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

Links

Crossrefs

Cf. A055595, A070783, A070784, A070785, A070787.

A070783 Square of longest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

Original entry on oeis.org

4, 5, 5, 8, 8, 9, 10, 10, 10, 10, 12, 13, 13, 13, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29
Offset: 1

Views

Author

Henry Bottomley, May 07 2002

Keywords

Examples

			a(6)=9 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

Links

Crossrefs

Cf. A055592, A070784, A070785, A070786, A070787.

A070784 Square of second longest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

Original entry on oeis.org

2, 4, 5, 4, 5, 8, 4, 8, 10, 10, 6, 5, 8, 9, 12, 15, 5, 8, 10, 13, 13, 5, 8, 13, 16, 17, 10, 16, 8, 9, 10, 10, 13, 13, 16, 17, 17, 17, 18, 20, 20, 12, 15, 8, 13, 13, 16, 17, 17, 20, 20, 25, 10, 10, 16, 18, 20, 20, 20, 26, 24, 14, 9, 13, 16, 20, 20, 20, 25, 25, 29, 12, 24, 30, 30, 10
Offset: 1

Views

Author

Henry Bottomley, May 07 2002

Keywords

Examples

			a(6)=8 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

Links

Crossrefs

Cf. A055593, A070783, A070785, A070786, A070787.

A070785 Square of shortest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

Original entry on oeis.org

2, 1, 4, 4, 1, 5, 2, 2, 4, 8, 6, 4, 1, 4, 3, 12, 5, 8, 2, 5, 13, 4, 5, 8, 1, 4, 4, 10, 4, 5, 2, 10, 1, 5, 4, 1, 9, 13, 2, 8, 16, 12, 3, 5, 4, 8, 9, 4, 16, 1, 5, 20, 4, 8, 2, 8, 2, 10, 18, 4, 15, 14, 8, 4, 5, 1, 13, 17, 4, 8, 16, 6, 6, 12, 24, 10, 5, 16, 9, 4, 1, 17, 10, 26, 5, 8, 10, 4, 2, 10, 4
Offset: 1

Views

Author

Henry Bottomley, May 07 2002

Keywords

Examples

			a(6)=5 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

Links

Crossrefs

Cf. A055594, A070783, A070784, A070786, A070787.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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