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A085365
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Decimal expansion of polygon-inscribing constant.
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2
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1, 1, 4, 9, 4, 2, 0, 4, 4, 8, 5, 3, 2, 9, 6, 2, 0, 0, 7, 0, 1, 0, 4, 0, 1, 5, 7, 4, 6, 9, 5, 9, 8, 7, 4, 2, 8, 3, 0, 7, 9, 5, 3, 3, 7, 2, 0, 0, 8, 6, 3, 5, 1, 6, 8, 4, 4, 0, 2, 3, 3, 9, 6, 5, 1, 8, 9, 6, 6, 0, 1, 2, 8, 2, 5, 3, 5, 3, 0, 5, 1, 1, 7, 7, 9, 4, 0, 7, 7, 2, 4, 8, 4, 9, 8, 5, 8, 3, 6, 9, 9, 3
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OFFSET
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0,3
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COMMENTS
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Inscribe an equilateral triangle in a circle of unit radius. Inscribe a circle in the triangle. Inscribe a square in the second circle and inscribe a circle in the square. Inscribe a regular pentagon in the third circle and so on. The radii of the circles converge to Product_{ k = 3..infinity } cos(Pi/k), which is this number. - N. J. A. Sloane, Feb 10 2008
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REFERENCES
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Dick Katz, Problem 91:24, in R. K. Guy, ed., Western Number Theory Problems, 1992-12-19 & 22.
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LINKS
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Table of n, a(n) for n=0..101.
Clive J. Grimstone, A product of cosines, Math. Gaz. 64 (428) (1980) 120-121.
R. Stephens, Slowly converging infinite products, Math. Gaz. 79 (486) (1995) 561-565.
Eric Weisstein's World of Mathematics, Polygon Inscribing
Wikipedia, Kepler-Bouwkamp constant
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FORMULA
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The log of this constant is equal to Sum_{n=1..infinity} ((2^(2n)-1)/n)*zeta(2n)*(zeta(2n)-1-1/2^(2n)). [Richard McIntosh] - N. J. A. Sloane, Feb 10 2008
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EXAMPLE
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0.1149420448532...
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CROSSREFS
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Equals 1/A051762.
Cf. A131671.
Sequence in context: A143298 A177839 A013669 * A019767 A021091 A096415
Adjacent sequences: A085362 A085363 A085364 * A085366 A085367 A085368
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KEYWORD
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nonn,cons
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AUTHOR
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Eric W. Weisstein, Jun 25 2003
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STATUS
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approved
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