A120211 x values giving the smallest integer solutions of y^2 = x*(a^N - x)*( b^N + x) (elliptic curve, Weierstrass equation) with a and b legs in primitive Pythagorean triangles and N = 2. Sequence ordered in increasing values of leg a. Relevant y values in A120210.

4, 6, 12, 24, 15, 40, 60, 40, 70, 84, 72, 56, 126, 144, 180, 168, 198, 180, 220, 264, 126, 286, 312, 364, 360, 390, 420, 480, 510, 49, 544, 300, 612, 616, 646, 684, 720, 760, 288, 798, 840, 924, 726, 966, 700, 1012, 1104, 990, 1150, 1200

Offset

1,1

References

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 47.

Links

Table of n, a(n) for n=1..50.

Example

First primitive Pythagorean triad: 3, 4, 5
Weierstrass equation. y^2 = x*( 3^2 - x)*( 4^2 + x)
Smallest integer solution (x, y) = (4,20)
First element in the sequence x = 4

Maple

flag :=1; x:=0; # a, b, c primitive Pythagorean triad while flag =1 do x:=x+1; y2:= x*( a^2 - x)*(x+b^2); if ((floor(sqrt(y2)))^2=y2)then print( x); flag :=0; fi; od;

Crossrefs

Cf. A009003, A020884, A120210-A120213.

Sequence in context: A307189 A054167 A303198 * A308471 A357809 A162688

Adjacent sequences: A120208 A120209 A120210 * A120212 A120213 A120214

Keyword

nonn

Author

Giorgio Balzarotti, Paolo P. Lava, Jun 10 2006

Status

approved