A244054 Decimal expansion of the maximal circumradius of a planar convex set containing no lattice point except for the origin where it has its circumcenter, and not protruding in opposite directions outside the square max(|x|,|y|) < 1 unless it protrudes significantly elsewhere, too.

1, 6, 8, 4, 7, 1, 2, 7, 0, 9, 7, 5, 2, 0, 4, 0, 2, 8, 6, 1, 5, 1, 5, 2, 7, 3, 6, 3, 6, 2, 7, 2, 1, 8, 1, 7, 2, 8, 2, 4, 8, 1, 2, 9, 8, 9, 8, 9, 5, 1, 6, 4, 2, 5, 3, 9, 7, 2, 8, 4, 7, 1, 3, 4, 2, 7, 2, 0, 8, 5, 7, 0, 0, 5, 5, 1, 4, 3, 8, 2, 4, 3, 4, 7, 9, 1, 8, 9, 2, 5, 5, 3, 6, 4, 3, 9, 5, 9, 7, 4, 6, 9

Offset

1,2

Comments

From M. F. Hasler, Sep 23 2020: (Start)

Without the additional technical condition, the circumradius would be infinite as can be seen by taking a very long lozenge centered at the origin and thin enough to avoid all other lattice points. (Or say, the convex hull of { +-(1/2, H); +-(1/4H, 0) } as H -> oo.)

With these conditions, the maximizing convex set is an almost isosceles triangle having, e.g., (-1,-1) very near the midpoint of its base and the point (1,1) on one of its legs near the opposite vertex. (End)

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.19 Circumradius-Inradius Constants, p. 535-536.

Links

Table of n, a(n) for n=1..102.

P. W. Awyong and P. R. Scott, On the maximal circumradius of a planar convex set containing one lattice point, Bull. Austral. Math. Soc. 52 (1995) 137-151; MR 96g:52030, DOI: 10.1017/S0004972700014519.

Formula

One and only positive root of 5*x^6 - 15*x^4 + 3*x^2 - 2.

Example

1.6847127097520402861515273636272181728248...

Mathematica

r = Root[5*x^6 - 15*x^4 + 3*x^2 - 2, x, 2]; RealDigits[r, 10, 102] // First

Prog

(PARI) default(realprecision, N=100); print(r=solve(x=0, 99, 5*x^6-15*x^4+3*x^2-2)); digits(r\.1^N) \\ M. F. Hasler, Sep 21 2020

Crossrefs

Sequence in context: A321075 A234846 A371467 * A195701 A247038 A195492

Adjacent sequences: A244051 A244052 A244053 * A244055 A244056 A244057

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 18 2014

Extensions

Definition corrected and link added by M. F. Hasler, Sep 21 2020

Status

approved