A353701 Denominator of squared radius of smallest circle passing through exactly n integral points.

4, 18, 2, 18, 4, 242, 2, 18, 4, 242, 2, 98, 4, 18, 2, 578, 4, 578, 2, 242, 242, 98, 2, 18, 98, 18, 2, 722, 4, 98, 2, 162

Offset

2,1

Comments

Schinzel proved such a circle always exists, and the square of the radius of a circle passing through 3 integral points is always rational so the sequence is well-defined.

Links

Table of n, a(n) for n=2..33.

S. S. Lacerda, schinzel.py

E. Pegg, Lattice Circles

Jim Randell, A collection of minimal radius lattice circles (github)

C. Schinzel, Sur l'existence d'un cercle passant par un nombre donné de points aux coordonnées entières, Enseignement Math, vol. 4, pp. 71-72, 1958.

Example

For n=3 a minimal circle is (x - 1/6)^2 + (y - 1/6)^2 = 25/18.

Crossrefs

Numerators are A353700.

Sequence in context: A077275 A059903 A227540 * A246133 A205014 A204936

Adjacent sequences: A353698 A353699 A353700 * A353702 A353703 A353704

Keyword

nonn,nice,hard,frac

Author

Sofia Lacerda, May 04 2022

Extensions

Data corrected by Sean A. Irvine, Jul 19 2022

a(29)-a(33) from Jim Randell, Jan 10 2023

Status

approved