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%I #16 Aug 11 2021 20:24:35
%S 5,2,4,6,9,0,9,7,4,5,7,7,1,4,8,7,2,4,0,9,8,7,3,6,1,1,2,8,6,0,1,8,3,5,
%T 8,5,5,4,1,9,9,2,3,5,4,6,0,0,3,1,0,9,5,1,0,3,3,8,1,7,1,3,3,0,8,4,3,6,
%U 0,6,2,1,6,7,7,8,8,9,9,7,6,0,4,5,2,2,2,3,4,4,5,6,1,0,8,4,6,4,3
%N Decimal expansion of x satisfying x=e^(x-3).
%C See A202348 for a guide to related sequences. The Mathematica program includes a graph.
%e 0.052469097457714872409873611286018358554199...
%t u = 1; v = -3;
%t f[x_] := x; g[x_] := E^(u*x + v)
%t Plot[{f[x], g[x]}, {x, 0, .2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .15, .16}, WorkingPrecision -> 110]
%t RealDigits[r] (* A202494 *)
%t RealDigits[ -ProductLog[-1/E^3], 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%o (PARI) solve(x=0, 1, x-exp(x-3)) \\ _Michel Marcus_, Aug 11 2021
%Y Cf. A202348.
%K nonn,cons
%O -1,1
%A _Clark Kimberling_, Dec 20 2011
%E Offset corrected by _Georg Fischer_, Aug 10 2021
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