

A282279


Decimal expansion of minimal radius of a circle that contains 12 nonoverlapping unit disks.


1



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

1,1


LINKS

Matthew House, Table of n, a(n) for n = 1..10000
F. Fodor, The densest packing of 12 congruent circles in a circle, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 41 (2000), No. 2, 401409.


FORMULA

Set r as the greatest real root of x^5  3*x^4 + 7*x^2  15*x + 9 = 0. Then, A = 1 + 2*r/sqrt(3) = 4.029601930...


EXAMPLE

4.029601930116183497482741041263349896...


MATHEMATICA

r = Root[#^5  3 #^4 + 7 #^2  15 # + 9 &, 3];
N[1 + 2 r/Sqrt[3], 20]


PROG

(PARI) r = solve(x=2, 3, x^5  3*x^4 + 7*x^2  15*x + 9); 1 + 2*r/sqrt(3) \\ Michel Marcus, Feb 11 2017


CROSSREFS

Sequence in context: A011352 A275983 A285750 * A208333 A279413 A208748
Adjacent sequences: A282276 A282277 A282278 * A282280 A282281 A282282


KEYWORD

nonn,cons


AUTHOR

Matthew House, Feb 10 2017


STATUS

approved



