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A105199
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Decimal expansion of arctan(2).
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5
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1, 1, 0, 7, 1, 4, 8, 7, 1, 7, 7, 9, 4, 0, 9, 0, 5, 0, 3, 0, 1, 7, 0, 6, 5, 4, 6, 0, 1, 7, 8, 5, 3, 7, 0, 4, 0, 0, 7, 0, 0, 4, 7, 6, 4, 5, 4, 0, 1, 4, 3, 2, 6, 4, 6, 6, 7, 6, 5, 3, 9, 2, 0, 7, 4, 3, 3, 7, 1, 0, 3, 3, 8, 9, 7, 7, 3, 6, 2, 7, 9, 4, 0, 1, 3, 4, 1, 7, 1, 2, 8, 6, 8, 6, 1, 7, 0, 6, 4, 1, 4, 3, 4, 5, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| atan(2) + A073000 = pi/2
Contribution from Clark Kimberling (ck6(AT)evansville.edu), Feb 10 2009: (Start)
Arctan(2) is the (minimal) central angle of a regular icosahedron, which is
the platonic solid having 20 faces and 12 vertices. The (minimal) central
angle is AOB, where A and B are any neighboring pair of vertices and O is
the center. To evaluate AOB, it is helpful to start with 12 vertices:
(0,c*t,d), (d,0,c*t), (c*t,d,0) where c=(1 or -1) and d=(1 or -1) and t is
the golden ratio, (1+sqrt(5))/2. For neighboring vertices, one can select
(t,1,0) and (0,t,1). (End)
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LINKS
| G. Boros, V. Moll, Sums of arctangents and some formulae of Ramanujan, Sci. Ser. A Math. Sci 11 (2005) 13-24 [MR2196063] eq. (2.11). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 12 2010]
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FORMULA
| Equals sum_{k=1..infinity} arctan( 8k/(4k^4+5)) [Boros and Moll, from R. J. Mathar, Apr 12 2010]
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EXAMPLE
| 1.107148717794090503017065460...
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CROSSREFS
| Sequence in context: A201750 A198825 A073008 * A020791 A086210 A085467
Adjacent sequences: A105196 A105197 A105198 * A105200 A105201 A105202
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KEYWORD
| cons,nonn
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AUTHOR
| Bryan Jacobs (bryanjj(AT)gmail.com), Apr 12 2005
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EXTENSIONS
| Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 12 2010
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