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A165953
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Decimal expansion of (5*sqrt(3) + sqrt(15))/(6*Pi).
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4
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6, 6, 4, 9, 0, 8, 8, 9, 4, 2, 0, 5, 3, 2, 6, 6, 4, 3, 1, 1, 4, 4, 2, 8, 4, 4, 6, 7, 0, 8, 6, 3, 3, 7, 1, 6, 1, 6, 4, 8, 7, 6, 5, 8, 0, 5, 5, 5, 6, 9, 1, 9, 3, 8, 1, 0, 5, 7, 5, 9, 2, 6, 0, 5, 7, 2, 2, 9, 6, 4, 7, 1, 8, 1, 8, 7, 7, 3, 2, 5, 9, 7, 4, 9, 7, 0, 8, 9, 0, 0, 2, 6, 9, 2, 0, 9, 2, 5, 9, 8, 9, 8, 2, 8, 0
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OFFSET
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0,1
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COMMENTS
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The ratio of the volume of a regular dodecahedron to the volume of the circumscribed sphere (which has circumradius a*(sqrt(3) + sqrt(15))/4 = a*(A002194 + A010472)/4, where a is the dodecahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A049541, A165952, and A165954. A063723 shows the order of these by size.
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LINKS
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Table of n, a(n) for n=0..104.
Eric Weisstein's World of Mathematics, Dodecahedron.
Index entries for transcendental numbers.
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FORMULA
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Equals (5*A002194 + A010472)/(6*A000796).
Equals (5*A002194 + A010472)*A049541/6.
Equals (10*A010527 + A010472)*A049541/6.
Equals (5 + sqrt(5))/(2*Pi*sqrt(3)).
Equals (5 + A002163)*A049541*A020760/2.
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EXAMPLE
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0.6649088942053266431144284467086337161648765805556919381057592605722964718...
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MATHEMATICA
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RealDigits[(5*Sqrt[3]+Sqrt[15])/(6*Pi), 10, 120][[1]] (* Harvey P. Dale, Feb 16 2018 *)
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PROG
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(PARI) (5*sqrt(3)+sqrt(15))/(6*Pi)
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CROSSREFS
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Cf. A000796, A002194, A010472, A165922, A049541, A165952, A165954, A063723, A002163, A020760, A010527.
Sequence in context: A002421 A360828 A209938 * A045885 A019118 A019126
Adjacent sequences: A165950 A165951 A165952 * A165954 A165955 A165956
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KEYWORD
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cons,nonn
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AUTHOR
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Rick L. Shepherd, Oct 02 2009
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STATUS
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approved
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