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A248413
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Decimal expansion of theta_1, one of the angles associated with the bow-and-arrow configuration used in the 2-arc smallest length problem.
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3
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1, 2, 8, 6, 5, 1, 1, 2, 6, 7, 6, 3, 1, 0, 1, 2, 3, 0, 0, 8, 2, 6, 7, 8, 8, 5, 4, 0, 0, 3, 7, 0, 7, 8, 9, 3, 5, 5, 2, 9, 8, 2, 8, 3, 1, 9, 1, 6, 8, 2, 9, 5, 0, 9, 6, 2, 5, 6, 4, 5, 0, 6, 5, 2, 0, 9, 4, 8, 6, 3, 4, 9, 4, 2, 1, 8, 6, 9, 6, 5, 6, 1, 5, 5, 5, 5, 8, 0, 7, 1, 1, 6, 0, 1, 8, 7, 6, 8, 2, 9, 2, 7, 3
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OFFSET
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1,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.11 Beam detection constants, p. 516.
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LINKS
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Table of n, a(n) for n=1..103.
Bow-and-arrow configuration [From the book by Steven Finch]
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FORMULA
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theta_1 = 4*arctan(sqrt(x1)), where x1 is the second smallest positive root of x^10 + 65*x^9 - 2139*x^8 + 20476*x^7 - 78054*x^6 + 126214*x^5 - 78054*x^4 + 20476*x^3 - 2139*x^2 + 65*x + 1.
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EXAMPLE
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1.286511267631012300826788540037078935529828319168295...
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MATHEMATICA
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x1 = Root[x^10 + 65*x^9 - 2139*x^8 + 20476*x^7 - 78054*x^6 + 126214*x^5 - 78054*x^4 + 20476*x^3 - 2139*x^2 + 65*x + 1, x, 4]; theta1 = 4*ArcTan[Sqrt[x1]]; RealDigits[theta1, 10, 103] // First
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CROSSREFS
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Cf. A248414 (theta_2), A248415 (length upper bound).
Sequence in context: A028352 A132699 A347634 * A206099 A021353 A131361
Adjacent sequences: A248410 A248411 A248412 * A248414 A248415 A248416
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KEYWORD
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cons,nonn
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AUTHOR
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Jean-François Alcover, Oct 06 2014
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STATUS
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approved
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