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 1-6 of 6 results.

A084388 a(n) = least positive k such that k^2 - A080761(n) is a cube.

Original entry on oeis.org

3, 2, 3, 6, 47, 4, 5, 19, 12, 7, 5, 6, 83, 6, 10, 8, 37, 16, 7, 13, 7, 9, 28, 8, 11, 8, 24, 53, 1874, 14, 9, 302, 9, 33, 10, 11, 77, 21, 10, 15, 926, 13, 59, 48, 18, 29, 11, 12, 386, 11, 43, 71, 65, 16, 14, 12, 173, 22, 13, 12, 19, 97, 1076, 111, 34, 13, 190, 17, 13, 14, 30, 54
Offset: 1

Views

Author

Cino Hilliard, Jun 23 2003

Keywords

Crossrefs

A084389 a(n) = least positive k such that k^3 + A080761(n) is a square.

Original entry on oeis.org

2, 1, 1, 3, 13, 1, 2, 7, 5, 3, 1, 2, 19, 1, 4, 3, 11, 6, 2, 5, 1, 3, 9, 2, 4, 1, 8, 14, 152, 5, 2, 45, 1, 10, 2, 3, 18, 7, 1, 5, 95, 4, 15, 13, 6, 9, 2, 3, 53, 1, 12, 17, 16, 5, 4, 2, 31, 7, 3, 1, 6, 21, 105, 23, 10, 2, 33, 5, 1, 3, 9, 14, 6, 7, 2, 11, 4, 1, 84, 19, 3, 5, 13, 12, 2, 741, 1, 4
Offset: 1

Views

Author

Cino Hilliard, Jun 23 2003

Keywords

Crossrefs

A084387 Duplicate of A080761.

Original entry on oeis.org

1, 3, 8, 9, 12, 15, 17, 18, 19, 22, 24, 28, 30, 35, 36, 37, 38, 40, 41, 44, 48, 54, 55, 56, 57
Offset: 1

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Author

Keywords

A134042 Complete list of solutions to y^2 = x^3 + 113; sequence gives x values.

Original entry on oeis.org

-4, 2, 8, 11, 26, 422
Offset: 1

Views

Author

Artur Jasinski, Oct 03 2007

Keywords

Comments

For corresponding y values and examples see A134043.

Crossrefs

Programs

  • Magma
    Sort([ p[1] : p in IntegralPoints(EllipticCurve([0, 113])) ]); /* adapted from A029728 */
    
  • SageMath
    [i[0] for i in EllipticCurve([0, 113]).integral_points()] # Seiichi Manyama, Aug 25 2019

Extensions

Edited and corrected by Klaus Brockhaus, Oct 04 2007

A134043 Complete list of solutions to y^2 = x^3 + 113; sequence gives y values.

Original entry on oeis.org

7, 11, 25, 38, 133, 8669
Offset: 1

Views

Author

Artur Jasinski, Oct 03 2007

Keywords

Comments

For corresponding x values see A134043.

Examples

			a(1)^2 = 7^2 = 49 = A134042(1)^3 + 113 = -64 + 113.
a(2)^2 = 11^2 = 121 = A134042(2)^3 + 113 = 8 + 113.
a(3)^2 = 25^2 = 625 = A134042(3)^3 + 113 = 512 + 113.
a(4)^2 = 38^2 = 1444 = A134042(4)^3 + 113 = 1331+ 113.
a(5)^2 = 133^2 = 17689 = A134042(5)^3 + 113 = 17576 + 113.
a(6)^2 = 8669^2 = 75151561 = A134042(6)^3 + 113 = 75151448 + 113.
		

Crossrefs

Programs

  • Magma
    Sort([ Abs(p[2]) : p in IntegralPoints(EllipticCurve([0, 113])) ]); /* adapted from A029727 */
  • Mathematica
    (Program does not produce first two terms) a = {}; Do[k = n^2 - (Floor[n^(2/3)])^3; If[(k > 112) && (k < 113), AppendTo[a, n]], {n, 1, 100000}]; a

Extensions

Edited and corrected by Klaus Brockhaus, Oct 04 2007

A080762 Positive numbers not of the form y^2 - x^3, x and y >= 1.

Original entry on oeis.org

2, 4, 5, 6, 7, 10, 11, 13, 14, 16, 20, 21, 23, 25, 26, 27, 29, 31, 32, 33, 34, 39, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 58, 59, 60, 61, 62, 66, 67, 69, 70, 72, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 93, 95, 96, 102, 103, 104, 109, 110, 111, 114, 115
Offset: 1

Views

Author

Cino Hilliard, Mar 10 2003

Keywords

Comments

This is Mordell's equation with the condition that x and y are positive. Sequence A054504 lists the n for which there is no solution to Mordell's equation (positive or negative x and y). Hence, all of those numbers will be in this sequence. Additional terms of this sequence can be determined by looking at the link to Gebel's data. - T. D. Noe, Mar 23 2011

Crossrefs

Complement of A080761.

Programs

  • PARI
    diop(n,m) = {f=0; for(p=1,m, f=0; for(x=1,n, y=x*x*x+p; if(issquare(y),f=1); ); if(f==0,print1(p" ")) ) }
Showing 1-6 of 6 results.