cp's OEIS Frontend

A202355 Decimal expansion of the number x satisfying x-1=exp(-x).

%I A202355 #18 Feb 07 2025 16:44:07
%S A202355 1,2,7,8,4,6,4,5,4,2,7,6,1,0,7,3,7,9,5,1,0,9,3,5,8,7,3,9,0,2,2,9,8,0,
%T A202355 1,5,5,4,3,9,4,7,7,4,8,8,6,1,9,7,4,5,7,6,5,4,5,3,1,7,8,1,0,5,5,3,5,0,
%U A202355 2,9,3,7,5,4,5,9,9,4,9,8,9,8,1,9,2,0,4,9,8,4,2,8,1,1,2,9,9,4,2
%N A202355 Decimal expansion of the number x satisfying x-1=exp(-x).
%C A202355 See A202322 for a guide to related sequences. The Mathematica program includes a graph.
%H A202355 G. C. Greubel, <a href="/A202355/b202355.txt">Table of n, a(n) for n = 1..5000</a>
%F A202355 Equals A202357 + 1. - _Vaclav Kotesovec_, Jan 31 2015
%e A202355 x=1.2784645427610737951093587390229801554394...
%t A202355 u = 1; v = -1;
%t A202355 f[x_] := u*x + v; g[x_] := E^-x
%t A202355 Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}]
%t A202355 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A202355 RealDigits[r] (* A202355 *)
%t A202355 (* other program *)
%t A202355 RealDigits[1 + ProductLog[1/E], 10, 99] // First (* _Jean-François Alcover_, Feb 14 2013 *)
%o A202355 (PARI) 1 + lambertw(exp(-1)) \\ _G. C. Greubel_, Jun 10 2017
%Y A202355 Cf. A202322.
%K A202355 nonn,cons
%O A202355 1,2
%A A202355 _Clark Kimberling_, Dec 18 2011