|
Search: id:A118676
|
|
|
| A118676 |
|
Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+79)^2 = y^2. |
|
+0
9
|
|
| 0, 20, 161, 237, 341, 1140, 1580, 2184, 6837, 9401, 12921, 40040, 54984, 75500, 233561, 320661, 440237, 1361484, 1869140, 2566080, 7935501, 10894337, 14956401, 46251680, 63497040, 87172484, 269574737, 370088061, 508078661, 1571196900
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Also values x of Pythagorean triples (x, x+79, y).
Corresponding values y of solutions (x, y) are in A159758.
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) = (83+18*sqrt(2))/79 for n mod 3 = {1, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (10659+6110*sqrt(2))/79^2 for n mod 3 = 0.
|
|
FORMULA
|
a(n) = 6*a(n-3)-a(n-6)+158 for n > 6; a(1)=0, a(2)=20, a(3)=161, a(4)=237, a(5)=341, a(6)=1140.
G.f.: x*(20+141*x+76*x^2-16*x^3-47*x^4-16*x^5)/((1-x)*(1-6*x^3+x^6)).
a(3*k+1) = 79*A001652(k) for k >= 0.
|
|
PROGRAM
|
(PARI) {forstep(n=0, 100000000, [1, 3], if(issquare(2*n^2+158*n+6241), print1(n, ", ")))}
|
|
CROSSREFS
|
Cf. A159758, A028871, A118337, A001652, A156035 (decimal expansion of 3+2*sqrt(2)), A159759 (decimal expansion of (83+18*sqrt(2))/79), A159760 (decimal expansion of (10659+6110*sqrt(2))/79^2).
Sequence in context: A059601 A125357 A126515 this_sequence A067534 A041768 A056114
Adjacent sequences: A118673 A118674 A118675 this_sequence A118677 A118678 A118679
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mohamed Bouhamida (bhmd95(AT)yahoo.fr), May 19 2006
|
|
EXTENSIONS
|
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2009
|
|
|
Search completed in 0.002 seconds
|
