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A019913
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Decimal expansion of tangent of 15 degrees.
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5
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2, 6, 7, 9, 4, 9, 1, 9, 2, 4, 3, 1, 1, 2, 2, 7, 0, 6, 4, 7, 2, 5, 5, 3, 6, 5, 8, 4, 9, 4, 1, 2, 7, 6, 3, 3, 0, 5, 7, 1, 9, 4, 7, 4, 6, 1, 8, 9, 6, 1, 9, 3, 7, 1, 9, 4, 4, 1, 9, 3, 0, 2, 0, 5, 4, 8, 0, 6, 6, 9, 8, 3, 0, 9, 1, 1, 9, 9, 9, 6, 2, 9, 1, 8, 8, 5, 3, 8, 1, 3, 2, 4, 2, 7, 5, 1, 4, 2, 4
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OFFSET
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0,1
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COMMENTS
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Also, 2 - sqrt(3) = cotangent of 75 degrees. An equivalent definition of this sequence: decimal expansion of x < 1 satisfying x^2 - 4*x + 1 = 0. - Arkadiusz Wesolowski, Nov 29 2011
Multiplied by -1 (that is, -2 + sqrt(3)), this is one of three real solutions to x^3 = 15x + 4. The other two are 4 and -2 - sqrt(3), all of which can be found with Viete's formula. - Alonso del Arte, Dec 15 2012
Wentworth (1903) shows how to compute the tangent of 15 degrees to five decimal places by the laborious process of adding up the first few terms of Pi/12 + Pi^3/5184 + 2Pi^5/3732480 + 17Pi^7/11287019520 + ... - Alonso del Arte, Mar 13 2015
This is the radius of the largest sphere that can be placed in the space between a sphere of radius 1 and the corners of its circumscribing cube. - Amiram Eldar, Jul 11 2020
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REFERENCES
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Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1). Princeton, New Jersey: Princeton University Press (1988): 22 - 23.
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LINKS
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FORMULA
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Equals Sum_{k>=1} binomial(2*k,k)/(6^k*(k+1)). - Amiram Eldar, Jul 11 2020
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EXAMPLE
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0.2679491924311227064725536...
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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