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A281115
Decimal expansion of the greatest minimal separation between ten points in a unit circle.
1
7, 1, 0, 9, 7, 8, 2, 3, 5, 5, 6, 1, 2, 4, 6, 5, 5, 0, 8, 3, 0, 7, 2, 5, 9, 7, 6, 9, 0, 2, 6, 8, 7, 2, 5, 3, 4, 9, 3, 9, 6, 8, 5, 9, 6, 3, 1, 3, 8, 0, 9, 4, 6, 9, 7, 9, 8, 3, 2, 4, 1, 8, 3, 4, 2, 5, 2, 7, 3, 7, 9, 5, 5, 1, 6, 5, 3, 4, 0, 4, 5, 5, 5, 1, 9, 9, 5, 5, 6, 1, 0, 6, 5, 3, 3, 4, 9, 5, 9, 1, 3, 3
OFFSET
0,1
COMMENTS
The corresponding values for two to nine points are all of the form 2*sin(Pi/k), where k is the number of points N for N <= 6 and N-1 for N > 6. The value for ten points is the first that cannot be expressed in this form with k an integer, although it is still algebraic of degree 24.
The smallest circle ten unit circles will fit into has radius r = 1 + 2/d = 3.81302563... and the maximum radius of ten non-overlapping circles in the unit circle is 1 / r = 0.26225892...
FORMULA
d is the smallest positive root of d^24 - 32*d^22 + 463*d^20 - 3998*d^18 + 22899*d^16 - 91428*d^14 + 260179*d^12 - 529874*d^10 + 763206*d^8 - 754052*d^6 + 481476*d^4 - 176440*d^2 + 27556.
EXAMPLE
0.71097823556124655083072597690268...
PROG
(PARI) p = Pol([1, 0, -32, 0, 463, 0, -3998, 0, 22899, 0, -91428, 0, 260179, 0, -529874, 0, 763206, 0, -754052, 0, 481476, 0, -176440, 0, 27556]); polrootsreal(p)[5]
CROSSREFS
Cf. A281065 (10 points in unit square).
Sequence in context: A324007 A176442 A361602 * A370363 A249776 A348970
KEYWORD
nonn,cons
AUTHOR
Jeremy Tan, Jan 14 2017
STATUS
approved