A030798 Decimal expansion of the solution to x^x = 2.

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

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• cons

Comments

The constant 1.559610469462... is transcendental. - Nick Hobson, Nov 29 2006

Examples

			1.559610469462369349970388768765002993284883511843091424719594569...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Nick Hobson, Solution to puzzle 29: x^x. Remark: x^x = 2.
• Gianni Sarcone, Zoo of Numbers: Numbers NaN to 6, Archimedes Lab, Genoa, Italy.
• Jonathan Sondow and Diego Marques, Algebraic and transcendental solutions of some exponential equations, arXiv:1108.6096 [math.NT], 2011; Annales Mathematicae et Informaticae 37 (2010) 151-164; see top of p. 4 in the link.
• Index entries for transcendental numbers

Crossrefs

Cf. A153510 (continued fraction), A199550 (x^x^x = 2).

Programs

Mathematica

RealDigits[ Log[2]/ProductLog[Log[2]], 10, 111][[1]] (* Robert G. Wilson v, Mar 23 2005 *)
RealDigits[x/.FindRoot[x^x==2,{x,1},WorkingPrecision->120]][[1]] (* Harvey P. Dale, May 27 2020 *)

PARI

solve(x=1, 2, x^x-2) \\ Michel Marcus, Jan 14 2015

PARI

log(2)/lambertw(log(2)) \\ Charles R Greathouse IV, May 14 2019

Formula

Equals log(2)/LambertW(log(2)). - Simon Plouffe, Mar 23 2005

Equals 1/A104748.

Extensions

Definition clarified by Jonathan Sondow, Sep 02 2011