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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
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 (list; graph; refs; listen; history; text; internal format)
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 A162688 A070232

Adjacent sequences:  A120208 A120209 A120210 * A120212 A120213 A120214

KEYWORD

nonn

AUTHOR

Giorgio Balzarotti, Paolo P. Lava, Jun 10 2006

STATUS

approved

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Last modified June 6 10:43 EDT 2020. Contains 334842 sequences. (Running on oeis4.)