A353701 - OEIS

%I #32 Jan 11 2023 11:08:33

%S 4,18,2,18,4,242,2,18,4,242,2,98,4,18,2,578,4,578,2,242,242,98,2,18,

%T 98,18,2,722,4,98,2,162

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

%C 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.

%H S. S. Lacerda, <a href="https://gist.github.com/SofiaSL/eca994e57e519ec16228fa754dd84fd1">schinzel.py</a>

%H E. Pegg, <a href="https://demonstrations.wolfram.com/LatticeCircles/">Lattice Circles</a>

%H Jim Randell, <a href="https://github.com/enigmatic-code/lattice_circles">A collection of minimal radius lattice circles</a> (github)

%H C. Schinzel, <a href="http://doi.org/10.5169/seals-34627">Sur l'existence d'un cercle passant par un nombre donné de points aux coordonnées entières</a>, Enseignement Math, vol. 4, pp. 71-72, 1958.

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

%Y Numerators are A353700.

%K nonn,nice,hard,frac

%O 2,1

%A _Sofia Lacerda_, May 04 2022

%E Data corrected by _Sean A. Irvine_, Jul 19 2022

%E a(29)-a(33) from _Jim Randell_, Jan 10 2023