cp's OEIS Frontend

A202500 Decimal expansion of x satisfying x=e^(-Pi*x).

%I A202500 #11 Feb 07 2025 16:44:07
%S A202500 3,4,1,7,5,6,0,1,7,7,8,5,8,5,6,3,9,6,8,3,1,2,6,7,1,6,6,7,7,1,7,0,5,8,
%T A202500 3,5,1,4,5,1,6,5,4,7,6,9,3,8,9,3,9,4,4,3,6,7,5,5,6,9,3,0,1,3,5,1,5,8,
%U A202500 2,9,7,2,2,5,1,1,9,8,9,1,2,2,4,6,7,5,1,3,1,3,8,5,9,8,8,1,3,1,2
%N A202500 Decimal expansion of x satisfying x=e^(-Pi*x).
%C A202500 See A202348 for a guide to related sequences. The Mathematica program includes a graph.
%e A202500 x=0.34175601778585639683126716677170583514516547...
%t A202500 u = -Pi; v = 0;
%t A202500 f[x_] := x; g[x_] := E^(u*x + v)
%t A202500 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A202500 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A202500 RealDigits[r]    (* A202500 *)
%t A202500 RealDigits[ ProductLog[Pi]/Pi, 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%Y A202500 Cf. A202348.
%K A202500 nonn,cons
%O A202500 0,1
%A A202500 _Clark Kimberling_, Dec 20 2011