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 1-7 of 7 results.

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

Cf. A152412, A177760, A177761, A177763, A177764, A177765, A177766.

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

Cf. A152412, A177760, A177761, A177764, A177765.

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

A177766 Terms of A177763 which have more than one such representation.

Original entry on oeis.org

7, 32, 207, 828, 1376, 1692, 2000, 2656, 3807, 5751, 5840, 7168, 7487, 7520, 7740, 7751, 18775, 19845, 20240, 21303, 22159, 23743, 25168, 29808, 30464, 30743, 32512, 32768, 34524, 38551, 45824, 46332, 47776, 49375, 53775, 54204
Offset: 1

Views

Author

Artur Jasinski, May 13 2010

Keywords

Examples

			    7 is a term:   7 = 2^5 -  5^2 and   7 =  8^5 - 181^2.
   32 is a term:  32 = 2^5 -  0^2 and  32 =  6^5 -  88^5.
  207 is a term: 207 = 3^5 -  6^2 and 207 =  6^5 -  87^2.
  828 is a term: 828 = 4^5 - 14^2 and 828 = 12^5 - 498^2.

Links

Crossrefs

Cf. A152412, A177760, A177761, A177764, A177765.

Extensions

More terms from Zak Seidov, May 14 2010
Edited by N. J. A. Sloane, May 15 2010

A179439 Positive numbers not of the form x^5 - y^2.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85
Offset: 1

Views

Author

Artur Jasinski, Jul 14 2010

Keywords

Examples

			19 can be expressed as 55^5 - 22434^2, so 19 is not in the sequence.

Crossrefs

Cf. A152412, A177760, A177761, A177764, A177765, A177859.

Extensions

Edited by Arkadiusz Wesolowski, Jan 05 2013

A177859 Complement of A152412.

Original entry on oeis.org

1, 2, 5, 6, 7, 9, 10, 12, 14, 16, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92
Offset: 1

Views

Author

Artur Jasinski, May 14 2010

Keywords

Crossrefs

Cf. A152412, A177760, A177761, A177763, A177764, A177765.

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

Cf. A152412, A177760, A177761, A177763, A177764, A177765, A177766, A177770.

Extensions

Added constraint s>0 to the definition - R. J. Mathar, May 23 2010

A177857 Possible values k such that hyperelliptic curve s^2+k=m^5 has at least 6 finite points.

Original entry on oeis.org

21303, 114143, 148507, 204732, 1044976, 15413568, 3369375, 3926151, 7019351, 7907868, 7942460, 9055625
Offset: 1

Views

Author

Artur Jasinski, May 14 2010

Keywords

References

  • Bremner A. 2008. On Equation Y^2=X^5+k. Experimental Mathematics, Vol. 17 No. 3 pp.371-374.

Crossrefs

Cf. A152412, A177760, A177761, A177763, A177764, A177765
Showing 1-7 of 7 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.