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 1-4 of 4 results.

A236330 Positive integers n such that x^2 - 14xy + y^2 + n = 0 has integer solutions.

Original entry on oeis.org

32, 48, 128, 176, 192, 288, 368, 416, 432, 512, 624, 704, 752, 768, 800, 944, 1056, 1136, 1152, 1184, 1200, 1328, 1472, 1568, 1584, 1664, 1712, 1728, 1776, 1952, 2048, 2096, 2208, 2288, 2336, 2352, 2496, 2592, 2672, 2816, 2864, 2928, 3008, 3056, 3072, 3104
Offset: 1

Views

Author

Colin Barker, Feb 16 2014

Keywords

Examples

			48 is in the sequence because x^2 - 14xy + y^2 + 48 = 0 has integer solutions, for example (x, y) = (2, 26).

Crossrefs

Cf. A001835 (n = 32), A001075 (n = 48), A237250 (n = 176), A003500 (n = 192), A082841 (n = 288), A151961 (n = 432), A077238 (n = 624).
Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236331.

A238240 Positive integers n such that x^2 - 20xy + y^2 + n = 0 has integer solutions.

Original entry on oeis.org

18, 35, 50, 63, 72, 74, 83, 90, 95, 98, 99, 107, 140, 162, 171, 200, 215, 227, 252, 266, 275, 288, 296, 315, 332, 347, 359, 360, 362, 371, 380, 387, 392, 395, 396, 407, 428, 450, 491, 495, 530, 539, 560, 567, 602, 623, 626, 635, 648, 666, 684, 695, 711, 722, 743, 747, 755, 770, 791, 794, 800, 810
Offset: 1

Views

Author

Colin Barker, Feb 20 2014

Keywords

Comments

Positive integers n such that x^2 - 99 y^2 + n = 0 has integer solutions. - Robert Israel, Oct 22 2024

Examples

			63 is in the sequence because x^2 - 20xy + y^2 + 63 = 0 has integer solutions, for example (x, y) = (1, 16).

Links

Crossrefs

Cf. A075839 (n = 18), A221763 (n = 63), A198947 (n = 90), A001085 (n = 99).
Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236330, A236331.

Programs

  • Maple
    filter:= t -> [isolve(99*y^2 - z^2 = t)] <> []:
select(filter, [$1..1000]); # Robert Israel, Oct 22 2024

Extensions

Corrected by Robert Israel, Oct 22 2024

A238245 Positive integers n such that x^2 - 22xy + y^2 + n = 0 has integer solutions.

Original entry on oeis.org

20, 39, 56, 71, 80, 84, 95, 104, 111, 116, 119, 120, 156, 180, 191, 224, 239, 255, 284, 296, 311, 320, 336, 351, 359, 380, 399, 404, 416, 431, 444, 455, 464, 471, 476, 479, 480, 500, 504, 551, 596, 599, 624, 639, 680, 695, 696, 719, 720, 756, 764, 791, 824
Offset: 1

Views

Author

Colin Barker, Feb 20 2014

Keywords

Examples

			39 is in the sequence because x^2 - 22xy + y^2 + 39 = 0 has integer solutions, for example (x, y) = (2, 43).

Crossrefs

Cf. A157014 (n = 20), A137881 (n = 104), A077422 (n = 120), A133275 (n = 180).
Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236330, A236331, A238240.

A261522 Positive integers k such that x^2 - 23xy + y^2 + k = 0 has integer solutions.

Original entry on oeis.org

21, 41, 59, 75, 84, 89, 101, 111, 119, 125, 129, 131, 164, 189, 201, 236, 251, 269, 300, 311, 329, 336, 356, 369, 381, 404, 419, 425, 444, 461, 476, 479, 489, 500, 509, 516, 521, 524, 525, 531, 579, 581, 629, 656, 675, 719, 731, 756, 761, 801, 804, 831, 839
Offset: 1

Views

Author

Colin Barker, Aug 23 2015

Keywords

Examples

			41 is in the sequence because x^2 - 23xy + y^2 + 41 = 0 has integer solutions; for example, (x, y) = (2, 45).

Crossrefs

Cf. A004253, A237254.
Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236330, A236331, A238240, A238245.
Showing 1-4 of 4 results.

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

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