A204098 Numbers n such that there is a triangle with area 1 and rational sides, and one side is the positive integer n.

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

Offset

1,1

Comments

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.

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

Links

Table of n, a(n) for n=1..20.

Example

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.

Crossrefs

Sequence in context: A030590 A047430 A360448 * A115838 A310572 A310573

Adjacent sequences: A204095 A204096 A204097 * A204099 A204100 A204101

Keyword

nonn,hard

Author

James R. Buddenhagen, Jan 10 2012

Status

approved