A342359 Decimal expansion of arctan(sqrt(Omega)), where Omega=LambertW(1) is the Omega constant.

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

Offset

0,1

Comments

The sine and the cosine of this angle appears in the values of two definite integrals that involve non-principal real branch of the Lambert W function, see A342360 and A342361.

Links

Table of n, a(n) for n=0..95.

Formula

Equals arctan(sqrt(LambertW(1))).

Example

0.6454752445650039244357315545660663652246772055940215161816...

Mathematica

Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[xi, 120]

Prog

(PARI) atan(sqrt(lambertw(1)))

Crossrefs

Cf. A342360, A342361, A030178.

Sequence in context: A021159 A106332 A247319 * A140246 A130786 A197295

Adjacent sequences: A342356 A342357 A342358 * A342360 A342361 A342362

Keyword

nonn,cons

Author

Gleb Koloskov, Mar 09 2021

Status

approved