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Numbers n such that there is a triangle with area 1 and rational sides, and one side is the positive integer n.
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%I #11 Jun 15 2013 15:09:51

%S 4,5,6,8,12,14,16,17,20,21,22,30,31,32,33,35,37,40,41,42

%N Numbers n such that there is a triangle with area 1 and rational sides, and one side is the positive integer n.

%C n is present in the sequence just in case the elliptic curve Y^2 = (n^4+4)*X^4 + 8*n^2*X^3 - 2*(n^4-4)*X^2 - 8*n^2*X + (n^4+4) has positive rank over the rationals. Note (X,Y)=(1,4) is a point on the curve.

%C Some entries in this sequence and some omissions from the sequence are based on standard conjectures about elliptic curves.

%e 5 is in the sequence because the rational triangle with sides (a, b, c) = (4097/858, 5, 401/858) has area 1 and one side is 5.

%K nonn,hard

%O 1,1

%A _James R. Buddenhagen_, Jan 10 2012