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

Author

Sofia Lacerda, May 04 2022

Keywords

• nonn
• nice
• hard
• frac

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.

Examples

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

Links

• 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.

Crossrefs

Numerators are A353700.

Extensions

Data corrected by Sean A. Irvine, Jul 19 2022

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