A248414 Decimal expansion of theta_2, one of the angles associated with the bow-and-arrow configuration used in the 2-arc smallest length problem.

1, 1, 9, 1, 0, 4, 7, 8, 2, 8, 5, 8, 5, 2, 0, 7, 3, 1, 2, 1, 8, 7, 6, 7, 7, 9, 4, 3, 0, 8, 6, 8, 4, 6, 3, 5, 0, 8, 0, 4, 6, 8, 3, 9, 5, 2, 6, 5, 3, 6, 9, 0, 9, 3, 1, 0, 7, 6, 3, 4, 3, 4, 7, 0, 5, 5, 7, 2, 4, 4, 0, 4, 6, 8, 7, 2, 2, 6, 9, 9, 1, 7, 2, 6, 1, 6, 8, 7, 9, 1, 8, 6, 2, 8, 4, 3, 3, 3, 6, 1, 2, 2, 8

Offset

1,3

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.

Formula

theta_2 = 2*arcsin(2*cos(theta_1)), where theta_1 is A248413.

Example

1.191047828585207312187677943086846350804683952653690931...

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]]; theta2 = 2*ArcSin[2*Cos[theta1]]; RealDigits[theta2, 10, 103] // First

Crossrefs

Cf. A248413 (theta_1), A248415 (length upper bound).

Sequence in context: A070060 A329085 A273636 * A176980 A227817 A372948

Adjacent sequences: A248411 A248412 A248413 * A248415 A248416 A248417

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 06 2014

Status

approved