A186503 Decimal expansion of the solution x to x^x = 13.

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

Offset

1,1

Links

Table of n, a(n) for n=1..102.

Formula

Equals log(13)/LambertW(log(13)). - Alois P. Heinz, Jun 16 2021

Example

2.6410619164843958084118390040657912549308732...

Mathematica

x=13; RealDigits[Log[x]/ProductLog[Log[x]], 10, 103][[1]]
RealDigits[x/.FindRoot[x^x==13, {x, 2.6}, WorkingPrecision->120], 10, 120][[1]] (* Harvey P. Dale, Feb 07 2025 *)

Crossrefs

Cf. A016636, A030798, A173158, A000038, A173159, A173160, A173161, A173162, A173163, A090625, A186501, A186502, A186504, A344930, A093590.

Sequence in context: A076393 A379953 A054674 * A213654 A213664 A059574

Adjacent sequences: A186500 A186501 A186502 * A186504 A186505 A186506

Keyword

nonn,cons,changed

Author

Vladimir Joseph Stephan Orlovsky, Feb 22 2011

Status

approved