A344905 Decimal expansion of the solution to x^x = sqrt(2).

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

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Formula

Equals log(2)/(2*LambertW(log(2)/2)). - Alois P. Heinz, Jun 02 2021

Example

1.304351178901036533647201231486234...

Mathematica

RealDigits[Log[Sqrt[2]]/ProductLog[Log[Sqrt[2]]], 10, 100][[1]] (* Amiram Eldar, Jun 02 2021 *)
RealDigits[x/.FindRoot[x^x==Sqrt[2], {x, 1}, WorkingPrecision-> 120], 10, 120][[1]] (* Harvey P. Dale, Jun 18 2021 *)

Prog

(PARI) solve(x=1, 2, x^x-sqrt(2)) \\ Hugo Pfoertner, Jun 02 2021

Crossrefs

Cf. A030798.

Sequence in context: A349915 A072480 A243920 * A181839 A100939 A099925

Adjacent sequences: A344902 A344903 A344904 * A344906 A344907 A344908

Keyword

cons,nonn

Author

Christoph B. Kassir, Jun 01 2021

Status

approved