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%I #4 Mar 31 2012 14:45:05
%S 4,6,12,24,15,40,60,40,70,84,72,56,126,144,180,168,198,180,220,264,
%T 126,286,312,364,360,390,420,480,510,49,544,300,612,616,646,684,720,
%U 760,288,798,840,924,726,966,700,1012,1104,990,1150,1200
%N 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.
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 47.
%e First primitive Pythagorean triad: 3, 4, 5
%e Weierstrass equation. y^2 = x*( 3^2 - x)*( 4^2 + x)
%e Smallest integer solution (x, y) = (4,20)
%e First element in the sequence x = 4
%p 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;
%Y Cf. A009003, A020884, A120210-A120213.
%K nonn
%O 1,1
%A Giorgio Balzarotti, _Paolo P. Lava_, Jun 10 2006
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