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 1-1 of 1 results.

A329808 Numbers k such that both k and k+1 are sums of a positive square and a positive cube.

Original entry on oeis.org

9, 36, 43, 72, 100, 126, 127, 128, 170, 196, 225, 232, 264, 289, 320, 350, 351, 352, 359, 368, 407, 424, 441, 442, 485, 486, 511, 512, 539, 576, 632, 656, 700, 703, 737, 784, 792, 810, 841, 848, 849, 872, 908, 953, 968, 1000, 1018, 1169, 1183, 1213, 1225, 1240, 1296
Offset: 1

Views

Author

Jianing Song, Nov 21 2019

Keywords

Comments

It is quite easy to give a constructive proof that this sequence is infinite. For example, 64*x^3 + 49*x^2 + 14*x + 1 = (7*x+1)^2 + (4*x)^3 and 64*x^3 + 49*x^2 + 14*x + 2 = (x+1)^2 + (4*x+1)^3. Moreover, if 97*x^2 + 2*x + 1 = y^2, then 64*x^3 + 49*x^2 + 14*x = y^2 + (4*x-1)^3. Obviously there are infinitely many solutions to 97*x^2 + 2*x + 1 = y^2, so there are infinitely many k such that k, k+1 and k+2 are all sums of a positive square and a positive cube.

Examples

			43 is a term because 43 = 4^2 + 3^3, 44 = 6^2 + 2^3.

Links

Crossrefs

Cf. A055394, A295787, A329807.

Programs

Showing 1-1 of 1 results.

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

Content is available under The OEIS End-User License Agreement.