A336002 Decimal expansion of the number u such that the arclength on y = tan(x) from (0,0) to (u, tan u) is 1.

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

Offset

0,1

Links

Table of n, a(n) for n=0..85.

Example

u = 0.6767706953243014485574475264257713407176...

Mathematica

x = x /. FindRoot[(Sqrt[2] (ArcSin[Sin[x]/Sqrt[2]] +
       ArcTanh[(Sqrt[2] Sin[x])/Sqrt[3 + Cos[2 x]]]) Cos[x] Sqrt[
     1 + Sec[x]^2])/Sqrt[3 + Cos[2 x]] == 1, {x, 1},
   WorkingPrecision -> 200]
RealDigits[x][[1]]

Crossrefs

Cf. A332633, A336003.

Sequence in context: A199079 A010723 A244588 * A223172 A340153 A368476

Adjacent sequences: A335999 A336000 A336001 * A336003 A336004 A336005

Keyword

nonn,cons

Author

Clark Kimberling, Jul 06 2020

Status

approved