Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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