login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120336 Number of solutions (x,y) of Diophantine equation y^2 = x*(a^N - x)*(b^N + x) (Weierstrass elliptic equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg "a". 0
1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Triads a = 3, b = 4, c = 5 and a = 4, b = 3, c = 5 provide different results for (x,y).
LINKS
EXAMPLE
First primitive Pythagorean triad: 3, 4, 5.
Weierstrass equation: y^2 = x*(3^2 - x)*(4^2 + x).
Unique integer solution: (x,y) = (4,20).
First element in the sequence: 1.
Fifth primitive Pythagorean triad: 8, 15, 17.
Integer solutions: (x,y) = (15, 420) and (30, 510).
Fifth element in the sequence: 2.
MAPLE
# a, b, c primitive Pythagorean triad n_sol:=0; for x from 1 by 1 to a^2 do y2:= x*( a^2 - x)*( x+ b^2); if ((floor(sqrt(y2)))^2=y2) n_sol:=n_sol+1; fi; print(n_sol) ; od;
CROSSREFS
Sequence in context: A117456 A030621 A284582 * A284558 A294623 A337473
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)