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.

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

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: A028352 A132699 A347634 * A206099 A021353 A131361

Adjacent sequences: A248410 A248411 A248412 * A248414 A248415 A248416

Keyword

cons,nonn

Author

Jean-François Alcover, Oct 06 2014

Status

approved