A128006 Numerators of rational-valued radii of circles given by 3 distinct integer points in the euclidean plane.

1, 5, 5, 2, 17, 13, 5, 13, 29, 3, 37, 25, 13, 10, 17, 25, 15, 53, 65, 4, 65, 41, 29, 25, 17, 13, 41, 73, 65, 85, 5, 101, 61, 41, 26, 37, 85, 97, 65, 109, 61, 89, 325, 17, 125, 29, 53, 65, 6, 145, 85, 61, 37, 137, 25, 51, 13, 85, 205, 73, 173, 533, 20, 34, 89, 7, 197, 169, 113, 85

Offset

1,2

Comments

A triangle in the Euclidean plane defines a circumcircle. There exist only certain rational-valued circumradii if the vertices of the triangle have integer coordinates. They are rendered by the pair of sequences A128006/A128007 in increasing order.

Links

Table of n, a(n) for n=1..70.

Crossrefs

See A128007 for denominators.

Cf. A128008, A128009, A128010, A128011, A192493, A192494.

Sequence in context: A023580 A021648 A287746 * A157703 A332507 A242617

Adjacent sequences: A128003 A128004 A128005 * A128007 A128008 A128009

Keyword

frac,nonn

Author

Heinrich Ludwig, Feb 11 2007

Status

approved