cp's OEIS Frontend

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

%I A226278 #32 Jul 16 2025 01:14:37
%S A226278 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,
%T A226278 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,
%U A226278 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
%N A226278 Decimal expansion of the number x > 1 defined by 2*log(x) = x - 1.
%C A226278 There are two solutions to the equation 2*log(x) = x - 1: {1, 3.51286...}.
%C A226278 Apart from the leading digit the same as A201890. - _R. J. Mathar_, Jun 05 2013
%F A226278 Equals 1 + A201890.
%F A226278 Equals exp(-LambertW_-1(-1/(2*sqrt(e)))-1/2). - _Natalia L. Skirrow_, Jul 13 2025
%F A226278 Equals 1/A101314 = exp(A202343). - _Hugo Pfoertner_, Jul 13 2025
%e A226278 x = 3.512862417252339353965475233218432653832833663402647422251789454...
%p A226278 Digits := 100; evalf([solve(2*ln(n)=n-1,n)]);
%t A226278 RealDigits[x /. FindRoot[2*Log[x] == x - 1, {x, 3.5}, WorkingPrecision -> 110]][[1]]
%t A226278 RealDigits[N[Exp[-ProductLog[-1,-1/(2*Sqrt[E])]-1/2],110]][[1]] (* _Natalia L. Skirrow_, Jul 13 2025 *)
%o A226278 (PARI) solve(x=3,4,2*log(x)-x+1) \\ _Charles R Greathouse IV_, Jun 05 2013
%Y A226278 Cf. A101314, A201890, A202343.
%K A226278 nonn,cons
%O A226278 1,1
%A A226278 _José María Grau Ribas_, Jun 02 2013