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

1,1

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

Links

Table of n, a(n) for n=1..105.

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

Example

x = 3.512862417252339353965475233218432653832833663402647422251789454...

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 *)

Prog

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

Crossrefs

Cf. A101314, A201890, A202343.

Sequence in context: A190178 A010261 A281494 * A005699 A127250 A350882

Adjacent sequences: A226275 A226276 A226277 * A226279 A226280 A226281

Keyword

nonn,cons

Author

José María Grau Ribas, Jun 02 2013

Status

approved