A128008 Numerators of rational-valued radii of circles given by 3 distinct integer points in the 3-dimensional Euclidean space.

1, 5, 3, 5, 11, 2, 17, 13, 9, 7, 33, 5, 13, 21, 27, 17, 29, 3, 37, 25, 19, 13, 33, 10, 17, 41, 7, 25, 29, 51, 11, 15, 53, 19, 99, 65, 23, 27, 4, 65, 57, 49, 41, 33, 29, 25, 21, 59, 17, 43, 69, 13, 53, 31, 9, 41, 73, 83, 37, 65, 14, 33, 85, 105, 43, 67, 77, 29, 63, 69, 89, 5

Offset: 1

Author

Heinrich Ludwig, Feb 14 2007

Keywords

• frac
• nonn

Comments

A triangle in the 3-dimensional Euclidean space 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 A128008/A128009 in increasing order.

Crossrefs

See A128009 for denominators. Cf. A128006, A128007, A128010, A128011.