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A248413 Decimal expansion of theta_1, one of the angles associated with the bow-and-arrow configuration used in the 2-arc smallest length problem. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.11 Beam detection constants, p. 516.

LINKS

Table of n, a(n) for n=1..103.

Bow-and-arrow configuration [From the book by Steven Finch]

FORMULA

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.

EXAMPLE

1.286511267631012300826788540037078935529828319168295...

MATHEMATICA

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

CROSSREFS

Cf. A248414 (theta_2), A248415 (length upper bound).

Sequence in context: A146943 A028352 A132699 * A206099 A021353 A131361

Adjacent sequences:  A248410 A248411 A248412 * A248414 A248415 A248416

KEYWORD

cons,nonn

AUTHOR

Jean-Fran├žois Alcover, Oct 06 2014

STATUS

approved

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Last modified October 16 08:15 EDT 2019. Contains 328051 sequences. (Running on oeis4.)