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.

A077059 Numbers j such that j^2 + k^2 is a cube for some k > j.

Original entry on oeis.org

0, 2, 5, 7, 9, 10, 16, 17, 18, 26, 30, 35, 36, 37, 38, 40, 44, 47, 50, 51, 54, 56, 58, 60, 65, 72, 73, 74, 75, 80, 82, 88, 95, 97, 101, 102, 106, 107, 115, 122, 128, 130, 135, 136, 140, 142, 143, 144, 145, 146, 150, 154, 164, 170, 174, 182, 187, 189, 190
Offset: 1

Views

Author

Zak Seidov, Oct 23 2002, Jan 02 2008

Keywords

Comments

The values of minimal k in A077060 and A077061. The values of corresponding c in A077062.

Examples

			2 is in the sequence because 2^2 + 11^2 = 5^3;
7 is in the sequence because 7^2 + 524^2 = 65^3;
1 is not in the sequence because 1^2 + k^2 is not a cube for any k > 1;
3 is not in the sequence because 3^2 + k^2 is not a cube for any k > 3.
174 is in the sequence because 174^2 + 406^2 = 58^3. - _Sean A. Irvine_, May 02 2025

Crossrefs

Cf. A076600, A077060, A077061, A077062.

Formula

j is in this sequence if for some integer k > j, j^2 + k^2 = c^3.

Extensions

Corrected and extended by Max Alekseyev, Dec 14 2011
Missing 174 inserted by Sean A. Irvine, May 02 2025

A077060 Smallest k>A077059(n) such that A077059(n)^2+k^2 is a cube (=A077061(n)^3).

Original entry on oeis.org

8, 11, 10, 524, 46, 30, 88, 68, 26, 39, 2935, 120, 2681, 222, 10582, 80, 117, 52, 350, 782, 297, 4192, 145, 1745, 142, 368, 77964, 110, 100, 240, 738, 835, 1104490, 1405096, 1010, 170, 371, 198, 236, 1342, 704, 56303, 270, 544, 505, 551122, 1962
Offset: 1

Views

Author

Zak Seidov, Oct 23 2002

Keywords

Examples

			k(0)=8 because A077059(0)^2+k(0)^2=0^2+8^2=4^3; k(0)=1 if 1 is a full cube.

Crossrefs

Cf. A076600, A077059-A077062.

Formula

n^2+k^2=c^3, k>n.

Extensions

Corrected and extended by Max Alekseyev, Dec 14 2011

A077061 a(n) = ( A077059(n)^2 + A077060(n)^2 )^(1/3).

Original entry on oeis.org

4, 5, 5, 65, 13, 10, 20, 17, 10, 13, 205, 25, 193, 37, 482, 20, 25, 17, 50, 85, 45, 260, 29, 145, 29, 52, 1825, 26, 25, 40, 82, 89, 10685, 12545, 101, 34, 53, 37, 41, 122, 80, 1469, 45, 68, 65, 6722, 157, 40, 125, 50, 250, 58, 41, 50, 58, 74, 389, 585
Offset: 1

Views

Author

Zak Seidov, Oct 23 2002

Keywords

Examples

			a(1)=4 because A077059(1)^2+A077060(1)^2=0^2+8^2=4^3.

Crossrefs

Cf. A076600, A077059, A077060, A077062.

Extensions

Corrected and extended by Max Alekseyev, Dec 14 2011
Missing a(55) inserted by Sean A. Irvine, May 02 2025
Showing 1-3 of 3 results.

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

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