A103549 Decimal expansion of solution to x*3^x = 1.

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

Offset: 0

Author

Zak Seidov, Mar 23 2005

Keywords

• nonn
• cons

Examples

			0.54780862165409744645057540815102185034598933770148...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Power Tower.
• Wikipedia, Tetration.

Crossrefs

Cf. A104748, A103550, A103551, A103552, A103553, A103554, A103555, A103556, A103559, A103560.

Programs

Maple

x:= LambertW(log(3))/log(3):
s:= convert(evalf(x, 140), string):
seq(parse(s[n+2]), n=0..119);  # Alois P. Heinz, Dec 03 2014

Mathematica

RealDigits[x/.FindRoot[x 3^x==1,{x,.5},WorkingPrecision->120]][[1]] (* Harvey P. Dale, May 27 2012 *)
RealDigits[ProductLog[Log[3]]/Log[3], 10, 105][[1]] (* Amiram Eldar, May 04 2023 *)

Formula

x*3^x = 1.

x = (1/3)^(1/3)^(1/3)^... = LambertW(log(3))/log(3). - Alois P. Heinz, Dec 03 2014

Extensions

More terms from Harvey P. Dale, May 27 2012