|
Search: id:A137351
|
|
|
| A137351 |
|
Composite numbers n such that x^2 - n*y^2 represents -1. |
|
+0
2
|
|
| 10, 26, 50, 58, 65, 74, 82, 85, 106, 122, 125, 130, 145, 170, 185, 202, 218, 226, 250, 265, 274, 290, 298, 314, 325, 338, 346, 362, 365, 370, 394, 425, 442, 445, 458, 481, 485, 493, 530, 533, 538, 554, 565, 586, 610, 626, 629, 634, 685, 697, 698, 730, 746
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Number of terms less than or equal to 10^k for k=0 .. : 0, 1, 8, 71, 712, 6702, 63485, 602870,..., . Robert G. Wilson v.
|
|
REFERENCES
|
J. P. Robertson and K. R. Matthews, A continued fraction approach to a result of Feit, Amer. Math. Monthly, 115 (No. 4, 2008), 346-349.
|
|
LINKS
|
Robert G. Wilson v, Table of n, a(n) for n = 1..63485
Eric Weisstein's World of Mathematics, Pell Equation.
|
|
EXAMPLE
|
3^2 - 10*1^2 = -1, so 10 is a member.
4005^2 - 106*389^2 = -1, so 106 is a member.
|
|
MATHEMATICA
|
lst = {}; Do[ If[ !PrimeQ@ n && FindInstance[x^2 - n*y^2 == -1, {x, y}, Integers] != {}, AppendTo[lst, n]], {n, 2, 1000}]
|
|
CROSSREFS
|
For the primes with this property see A002313. A134406 is a subset.
Adjacent sequences: A137348 A137349 A137350 this_sequence A137352 A137353 A137354
Sequence in context: A054315 A113770 A044452 this_sequence A134406 A099978 A074789
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas, Apr 08 2008
|
|
EXTENSIONS
|
More terms from RGWv (rgwv(AT)rgwv.com), Jul 20 2008
|
|
|
Search completed in 0.003 seconds
|
