A128007 Denominators of rational-valued radii of circles given by 3 distinct integer points in the Euclidean plane.

1, 4, 3, 1, 8, 6, 2, 5, 10, 1, 12, 8, 4, 3, 5, 7, 4, 14, 17, 1, 16, 10, 7, 6, 4, 3, 9, 16, 14, 18, 1, 20, 12, 8, 5, 7, 16, 18, 12, 20, 11, 16, 58, 3, 22, 5, 9, 11, 1, 24, 14, 10, 6, 22, 4, 8, 2, 13, 31, 11, 26, 80, 3, 5, 13, 1, 28, 24, 16, 12, 26, 22, 7, 9, 4

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. The circumradii are rendered by the pair of sequences A128006/A128007 in increasing order.

Links

Table of n, a(n) for n=1..75.

Crossrefs

See A128006 for numerators.

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

Sequence in context: A332496 A038763 A200384 * A098458 A165914 A139621

Adjacent sequences: A128004 A128005 A128006 * A128008 A128009 A128010

Keyword

frac,nonn

Author

Heinrich Ludwig, Feb 11 2007

Status

approved