A226278 Decimal expansion of the number x > 1 defined by 2*log(x) = x - 1.

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

Offset: 1

Author

José María Grau Ribas, Jun 02 2013

Keywords

• nonn
• cons

Comments

There are two solutions to the equation 2*log(x) = x - 1: {1, 3.51286...}.

Apart from the leading digit the same as A201890. - R. J. Mathar, Jun 05 2013

Examples

			x = 3.512862417252339353965475233218432653832833663402647422251789454...
		

Crossrefs

Cf. A101314, A201890, A202343.

Programs

Maple

Digits := 100; evalf([solve(2*ln(n)=n-1,n)]);

Mathematica

RealDigits[x /. FindRoot[2*Log[x] == x - 1, {x, 3.5}, WorkingPrecision -> 110]][[1]]
RealDigits[N[Exp[-ProductLog[-1,-1/(2*Sqrt[E])]-1/2],110]][[1]] (* Natalia L. Skirrow, Jul 13 2025 *)

PARI

solve(x=3,4,2*log(x)-x+1) \\ Charles R Greathouse IV, Jun 05 2013

Formula

Equals 1 + A201890.

Equals exp(-LambertW_-1(-1/(2*sqrt(e)))-1/2). - Natalia L. Skirrow, Jul 13 2025

Equals 1/A101314 = exp(A202343). - Hugo Pfoertner, Jul 13 2025