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

1,2

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.

Links

Table of n, a(n) for n=1..72.

Crossrefs

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

Sequence in context: A114740 A330523 A361546 * A265800 A144386 A256787

Adjacent sequences: A128005 A128006 A128007 * A128009 A128010 A128011

Keyword

frac,nonn

Author

Heinrich Ludwig, Feb 14 2007

Status

approved