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%I #36 Jan 11 2023 11:08:51
%S 1,25,1,625,25,138125,5,4225,625,801125,25,1221025,15625,105625,65,
%T 185870425,4225,185870425,625,29641625,29641625,30525625,325,17850625,
%U 35409725,1221025,15625,3159797225,105625,763140625,1105,1346691125
%N Numerator 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 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a353/A353700.java">Java program</a> (github)
%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 Denominators are A353701.
%K nonn,hard,frac,nice
%O 2,2
%A _Sofia Lacerda_, May 04 2022
%E Data corrected by _Sean A. Irvine_, Jul 17 2022
%E a(29)-a(33) from _Jim Randell_, Jan 10 2023