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A093766
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Decimal expansion of Pi/(2*sqrt(3)).
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3
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9, 0, 6, 8, 9, 9, 6, 8, 2, 1, 1, 7, 1, 0, 8, 9, 2, 5, 2, 9, 7, 0, 3, 9, 1, 2, 8, 8, 2, 1, 0, 7, 7, 8, 6, 6, 1, 4, 2, 0, 3, 3, 1, 2, 4, 0, 4, 6, 3, 7, 0, 2, 8, 7, 7, 8, 4, 9, 4, 2, 4, 6, 7, 6, 9, 4, 0, 6, 1, 5, 9, 0, 5, 6, 3, 1, 7, 6, 9, 4, 1, 8, 4, 2, 0, 6, 2, 4, 9, 4, 1, 0, 6, 0, 3, 0, 0, 8, 4, 4, 2, 8
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Circle packing density.
The number gives the areal coverage (90.68.. percent) of the close hexagonal (densest) packing of circles in the plane. The hexagonal unit cell is a rhombus of side length 1 and height sqrt(3)/2; the area of the unit cell is sqrt(3)/2 and the four parts of circles add to an area of one circle of radius 1/2, which is Pi/4. - R. J. Mathar, Nov 22 2011
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REFERENCES
| Jolley, Summation of Series, Dover (1961), eq (84) on page 16.
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LINKS
| Eric Weisstein's World of Mathematics, Smoothed Octagon
Eric Weisstein's World of Mathematics, Circle Packing
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FORMULA
| Pi/(2*Sqrt[3]) = (5/6)(7/6)(11/12)(13/12)(17/18)(19/18)(23/24)(29/30)(31/30)..., where the numerators are primes > 3 and the denominators are the nearest multiples of 6.
Equals sum_{n>=1} 1/A134667(n). [Jolley]
Equals sum_{n>=0} (-1)^n/A124647(n) [Jolley eq 271]
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EXAMPLE
| 0.906899682117108925297039128821077866142033124046370287784942...
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CROSSREFS
| Sequence in context: A068467 A131223 A198213 * A097674 A196549 A173164
Adjacent sequences: A093763 A093764 A093765 * A093767 A093768 A093769
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KEYWORD
| nonn,cons,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 15 2004
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