|
Search: id:A129974
|
|
|
| A129974 |
|
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+937)^2 = y^2. |
|
+0
5
|
|
| 0, 627, 1128, 2811, 6188, 9027, 18740, 38375, 54908, 111503, 225936, 322295, 652152, 1319115, 1880736, 3803283, 7690628, 10963995, 22169420, 44826527, 63905108, 129215111, 261270408, 372468527, 753123120, 1522797795, 2170907928
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Also values x of Pythagorean triples (x, x+937, y).
Corresponding values y of solutions (x, y) are in A160209.
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (1179+506*sqrt(2))/937 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (933747+224782*sqrt(2))/937^2 for n mod 3 = 0.
|
|
FORMULA
|
a(n) = 6*a(n-3)-a(n-6)+1874 for n > 6; a(1)=0, a(2)=627, a(3)=1128, a(4)=2811, a(5)=6188, a(6)=9027.
G.f.: x*(627+501*x+1683*x^2-385*x^3-167*x^4-385*x^5) / ((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 937*A001652(k) for k >= 0.
|
|
PROGRAM
|
(PARI) {forstep(n=0, 10000000, [3, 1], if(issquare(2*n^2+1874*n+877969), print1(n, ", ")))}
|
|
CROSSREFS
|
Cf. A160209, A001652, A129857, A156035 (decimal expansion of 3+2*sqrt(2)), A160210 (decimal expansion of (1179+506*sqrt(2))/937), A160211 (decimal expansion of (933747+224782*sqrt(2))/937^2).
Sequence in context: A031728 A098262 A031523 this_sequence A031703 A158382 A098260
Adjacent sequences: A129971 A129972 A129973 this_sequence A129975 A129976 A129977
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Jun 13 2007
|
|
EXTENSIONS
|
Edited and two terms added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 18 2009
|
|
|
Search completed in 0.005 seconds
|
