A173164 Decimal expansion of the constant which yields Catalan's constant if raised to itself.

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

Equals log(Catalan)/LambertW(log(Catalan)). - Alois P. Heinz, Aug 26 2018

Example

0.907839962...^0.907839962... = 0.915965594... = A006752.

Mathematica

x=Catalan; RealDigits[Log[x]/ProductLog[Log[x]], 10, 6! ][[1]]
RealDigits[x/.FindRoot[x^x==Catalan, {x, 1}, WorkingPrecision->120]][[1]] (* Harvey P. Dale, Jan 24 2015 *)

Prog

(PARI) solve(x=.5, 1, x^x - Catalan) \\ Michel Marcus, Aug 26 2018

Crossrefs

Cf. A006752 (Catalan's constant).

Sequence in context: A372830 A309823 A196549 * A298743 A181446 A097669

Adjacent sequences: A173161 A173162 A173163 * A173165 A173166 A173167

Keyword

nonn,cons

Author

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

Status

approved