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 1-5 of 5 results.

A177764 a(n) = smallest possible value of m corresponding to A177763(n).

Original entry on oeis.org

1, 2, 2, 3, 55, 2, 2, 2, 2, 3, 76, 4, 3, 3, 5, 3, 4, 3, 10, 3, 7, 3, 4, 3, 3, 5, 3, 3, 3, 3, 4, 3, 3, 11, 4, 5, 377, 4, 8, 6, 4, 13, 5, 7, 4, 9, 4, 5, 14, 4, 6, 4, 42, 4, 5, 4, 7, 4, 6, 5, 8, 22, 15, 4, 4, 10, 4, 5, 4, 4, 4, 6, 4, 5, 4, 7, 4, 4, 9, 4, 4, 4
Offset: 1

Views

Author

Artur Jasinski, May 13 2010

Keywords

Crossrefs

Extensions

Edited by N. J. A. Sloane, May 15 2010

A177765 a(n) = smallest possible value of s corresponding to A177763(n).

Original entry on oeis.org

0, 5, 4, 15, 22434, 3, 2, 1, 0, 14, 50354, 31, 13, 12, 55, 11, 30, 10, 316, 9, 129, 8, 29, 7, 6, 54, 5, 4, 3, 2, 28, 1, 0, 401, 27, 53, 2759646, 26, 180, 86, 25, 609, 52, 128, 24, 242, 23, 51, 733, 22, 85, 21, 11432, 20, 50, 19, 127, 18, 84, 49, 179, 2270, 871, 17, 16, 315
Offset: 1

Views

Author

Artur Jasinski, May 13 2010

Keywords

Crossrefs

Extensions

Edited by N. J. A. Sloane, May 15 2010

A177763 Numbers of the form m^5-s^2, m>=1, s >= 0.

Original entry on oeis.org

1, 7, 16, 18, 19, 23, 28, 31, 32, 47, 60, 63, 74, 99, 100, 122, 124, 143, 144, 162, 166, 179, 183, 194, 207, 209, 218, 227, 234, 239, 240, 242, 243, 250, 295, 316, 341, 348, 368, 380, 399, 412, 421, 423, 448, 485, 495, 524, 535, 540, 551, 583, 608, 624, 625
Offset: 1

Views

Author

Artur Jasinski, May 13 2010

Keywords

Comments

For values m see A177764.
For values s see A177765.
For numbers that have more than one representation see A177766.

Crossrefs

Programs

  • Mathematica
    aa = {}; bb = {}; cc = {}; Do[Do[If[((N[Sqrt[x^5 - n], 300] - Round[Sqrt[x^5 - n]])^2 < 10^-300) && (Im[Round[Sqrt[x^5 - n]]] == 0), AppendTo[aa, n]; AppendTo[bb, x]; AppendTo[cc, Round[Sqrt[x^5 - n]]]; Print[{n}, {x}, {Round[Sqrt[x^5 - n]]}]], {x, 1, 1000}], {n, 1, 1000}]; Union[aa]

Extensions

Edited by N. J. A. Sloane, May 15 2010

A177770 Conjectured positive numbers which have more than one representation (m,s) as a difference s^2 - m^5, m >= 1, s > 0.

Original entry on oeis.org

224, 356, 368, 433, 497, 657, 740, 1057, 1060, 1088, 1124, 1377, 1680, 1828, 2400, 2576, 3332, 3357, 3599, 4100, 4324, 4868, 7076, 8001, 8217, 10993, 11268, 11417, 12289, 13312, 14225, 14852, 15025, 15193, 15593, 15633, 17201, 19140, 20132, 20448, 21124
Offset: 1

Views

Author

Artur Jasinski, May 13 2010

Keywords

Comments

Warning: terms may be missing, see the Blomberg link.

Examples

			a(1) = 224 = 15^2-1^5 = 16^2-2^5.
a(2) = 356 = 59^2-5^5 = 182^2-8^5.
a(3) = 368 = 20^2-2^5 = 45531^2-73^5.
a(4) = 433 = 26^2-3^5 = 3447^2-26^5.
a(5) = 497 = 23^2-2^5 = 39^2-4^5.
a(6) = 657 = 30^2-3^5 = 41^2-4^5.
a(7) = 740 = 42^2-4^5 = 12842^2-44^5.
a(8) = 1057 = 332^2-2^5 = 1375^2-18^5.
a(9) = 1060 = 94^2-6^5 = 2822^2-24^5.
a(10) = 1088 = 33^2-1^5 = 184^2-8^5.
a(11) = 1124 = 34^2-2^5 = 318^2-10^5.
a(12) = 1377 = 49^2-4^5 = 1574^2-19^5.
a(13) = 1680 = 41^2-1^5 = 52^2-4^5.
a(14) = 1828 = 98^2-6^5 = 186^2-8^5 = 90298^2-96^5.
		

Crossrefs

Extensions

Added constraint s>0 to the definition, inserted 368 - R. J. Mathar, May 23 2010
Name clarified, a(25)-a(41) from Lars Blomberg, Aug 13 2013
Representations for a(3) added in Example by Lars Blomberg, Aug 13 2013

A177786 Positive numbers which have more than two representations (m,s) as a difference s^2-m^5, m>=1, s>0.

Original entry on oeis.org

1828, 3332, 4100
Offset: 1

Views

Author

Artur Jasinski, May 13 2010

Keywords

Comments

This sequence is a subsequence of A177770.
Contains also 10993 and 53668, not necessarily as the next terms. [R. J. Mathar, May 23 2010]

Examples

			a(1)=1828 = 98^2-6^5 = 186^2-8^5 = 90298^2-96^5.
a(2)=3332 = 58^2-2^5 = 66^2-4^5 = 190^2-8^5.
a(3)=4100 = 85^2-5^5 = 1026^2-16^5 = 1790^2-20^5.
		

Crossrefs

Extensions

Added constraint s>0 to the definition - R. J. Mathar, May 23 2010
Showing 1-5 of 5 results.