A353700 Numerator of squared radius of smallest circle passing through exactly n integral points.

1, 25, 1, 625, 25, 138125, 5, 4225, 625, 801125, 25, 1221025, 15625, 105625, 65, 185870425, 4225, 185870425, 625, 29641625, 29641625, 30525625, 325, 17850625, 35409725, 1221025, 15625, 3159797225, 105625, 763140625, 1105, 1346691125

Offset

2,2

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.

Sean A. Irvine, Java program (github)

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

Denominators are A353701.

Sequence in context: A232989 A040649 A104707 * A040618 A040619 A040617

Adjacent sequences: A353697 A353698 A353699 * A353701 A353702 A353703

Keyword

nonn,hard,frac,nice

Author

Sofia Lacerda, May 04 2022

Extensions

Data corrected by Sean A. Irvine, Jul 17 2022

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

Status

approved