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 A353701 Denominator of squared radius of smallest circle passing through exactly n integral points. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 7 05:42 EDT 2024. Contains 375729 sequences. (Running on oeis4.)