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 1-3 of 3 results.

A070067 Values of z in positive integer solutions of x^2 + y^5 = z^3, listed in increasing order of z.

Original entry on oeis.org

7, 117, 128, 320, 768, 832, 1120, 1153, 1226, 1296, 1377, 2500, 2592, 2816, 3168, 3888, 5760, 6561, 6948, 7168, 7776, 10625, 12960, 13968, 16514, 19208, 19926, 20240, 23652, 24384, 29158, 33614, 42768, 60100, 67228, 69984, 70400, 71199
Offset: 1

Views

Author

Dean Hickerson and Dan Asimov (asimov(AT)msri.org), Apr 18 2002

Keywords

Examples

			The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320) and (20480,32,768).

Crossrefs

x-values are in A070065, y-values are in A070066.

Programs

  • Mathematica
    For[z=1, True, z++, z3=z^3; For[y=1, (d=z3-y^5)>0, y++, If[IntegerQ[x=Sqrt[d]], Print[{x, y, z}]]]]

A070066 Values of y in positive integer solutions of x^2 + y^5 = z^3, listed in increasing order of z. (If a z-value occurs twice, list solutions in increasing order of y.)

Original entry on oeis.org

3, 9, 16, 16, 32, 48, 24, 6, 55, 72, 72, 100, 72, 112, 72, 108, 144, 162, 36, 192, 72, 100, 216, 72, 295, 343, 351, 359, 72, 368, 423, 343, 216, 300, 343, 648, 800, 783, 625, 833, 400, 450, 648, 972, 496, 576, 1024, 864, 675, 972, 1215, 242, 72, 500, 1176
Offset: 1

Views

Author

Dean Hickerson and Dan Asimov (asimov(AT)msri.org), Apr 18 2002

Keywords

Examples

			The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320) and (20480,32,768).

Crossrefs

x-values are in A070065, z-values are in A070067.

Programs

  • Mathematica
    For[z=1, True, z++, z3=z^3; For[y=1, (d=z3-y^5)>0, y++, If[IntegerQ[x=Sqrt[d]], Print[{x, y, z}]]]]

A103156 Numbers whose square can be expressed as the signed sum of a fifth power and a cube: z^2 = x^5 + y^3 with gcd(x,y,z)=1.

Original entry on oeis.org

3, 10, 411, 654, 7792, 36599, 39151, 647992, 1506463, 1525899, 2730128, 3353687, 4387861, 4942947, 5574720, 12092581, 128301258, 168454745, 184589480, 888155653, 20364997771, 53242416249, 65464918703, 73699708330, 74330984303
Offset: 1

Views

Author

Hugo Pfoertner, Jan 25 2005

Keywords

Examples

			a(1)=3 because 1^5 + 2^3 = 3^2;
a(2)=10 because (-3)^5 + 7^3 = 10^2;
a(3)=411 because 10^5 + 41^3 = 411^2;
a(4)=654 because 19^5 + (-127)^3 = 654^2.

Links

Crossrefs

Cf. A070065 positive integer solutions of x^2 + y^5 = z^3.
Showing 1-3 of 3 results.

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

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