|
| |
|
|
A193587
|
|
Numbers k such that quartic elliptic curve y^2 = 5x^4 - 4k have integer solutions.
|
|
0
|
|
|
|
1, 4, 11, 16, 19, 20, 25, 29, 31, 45, 59, 64, 71, 79, 81, 89, 95, 99, 101, 124, 131, 139, 151, 169, 176, 179, 181, 191, 199, 211, 220, 229, 239, 245, 251, 256, 271, 275, 284, 295, 304, 311, 316, 319, 320, 324, 349, 359, 361, 369, 379, 395, 400, 401, 439, 451
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
For such k existed such integers m that quintic trinomial x^5+k*x+m is reducible into cubic and quadratic factors.
Positive numbers of the form -d^4 + 3 d^2 e - e^2.
|
|
|
LINKS
|
Table of n, a(n) for n=1..56.
|
|
|
FORMULA
|
Complement to A193533.
|
|
|
MATHEMATICA
|
aa = {}; Do[Do[k = -d^4 + 3 d^2 e - e^2; If[k > 0, AppendTo[aa, k ]], {d, -100, 100}], {e, -100, 100}]; Take[Union[aa], 100]
|
|
|
CROSSREFS
|
Cf. A193524, A193528, A193531, A193533, A193584.
Sequence in context: A022131 A091391 A135105 * A072423 A156244 A020961
Adjacent sequences: A193584 A193585 A193586 * A193588 A193589 A193590
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Artur Jasinski, Jul 31 2011
|
|
|
STATUS
|
approved
|
| |
|
|
