|
Search: id:A130645
|
|
|
| A130645 |
|
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+439)^2 = y^2. |
|
+0
6
|
|
| 0, 44, 1121, 1317, 1541, 7644, 8780, 10080, 45621, 52241, 59817, 266960, 305544, 349700, 1557017, 1781901, 2039261, 9076020, 10386740, 11886744, 52899981, 60539417, 69282081, 308324744, 352850640, 403806620, 1797049361, 2056565301
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Also values x of Pythagorean triples (x, x+439, y).
Corresponding values y of solutions (x, y) are in A159890.
For the generic case x^2+(x+p)^2 = y^2 with p = m^2-2 a (prime) number > 7 in A028871, see A118337.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (443+42*sqrt(2))/439 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (450483+287918*sqrt(2))/439^2 for n mod 3 = 0.
|
|
FORMULA
|
a(n) = 6*a(n-3)-a(n-6)+878 for n > 6; a(1)=0, a(2)=44, a(3)=1121, a(4)=1317, a(5)=1541, a(6)=7644.
G.f.: x*(44+1077*x+196*x^2-40*x^3-359*x^4-40*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 439*A001652(k) for k >= 0.
|
|
PROGRAM
|
(PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+878*n+192721), print1(n, ", ")))}
|
|
CROSSREFS
|
Cf. A159890, A028871, A118337, A118675, A118676, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159891 (decimal expansion of (443+42*sqrt(2))/439), A159892 (decimal expansion of (450483+287918*sqrt(2))/439^2).
Sequence in context: A010996 A004423 A114170 this_sequence A004340 A004295 A063821
Adjacent sequences: A130642 A130643 A130644 this_sequence A130646 A130647 A130648
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 20 2007
|
|
EXTENSIONS
|
Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2009
|
|
|
Search completed in 0.002 seconds
|
