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A202323 Decimal expansion of the number x satisfying x+3=exp(-x).

%I A202323 #18 Feb 07 2025 16:44:07
%S A202323 7,9,2,0,5,9,9,6,8,4,3,0,6,7,7,0,0,1,4,1,8,3,9,5,8,7,7,8,8,5,4,2,2,0,
%T A202323 6,1,8,6,5,9,2,2,1,9,3,1,7,0,0,9,7,8,8,2,9,0,8,0,5,0,5,5,9,7,9,3,6,2,
%U A202323 7,3,7,2,1,0,8,5,5,1,5,4,5,7,3,2,8,1,5,0,0,8,7,3,2,3,8,3,5,4,0
%N A202323 Decimal expansion of the number x satisfying x+3=exp(-x).
%C A202323 See A202322 for a guide to related sequences. The Mathematica program includes a graph.
%H A202323 G. C. Greubel, <a href="/A202323/b202323.txt">Table of n, a(n) for n = 0..5000</a>
%H A202323 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A202323 x=-0.7920599684306770014183958778854220...
%t A202323 u = 3; v = 0;
%t A202323 f[x_] := u*x + v; g[x_] := E^x
%t A202323 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A202323 r = x /. FindRoot[f[x] == g[x], {x, 0.6, 0.7}, WorkingPrecision -> 110]
%t A202323 RealDigits[r] (* A202351 *)
%t A202323 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A202323 RealDigits[r] (* A202352 *)
%t A202323 (* other program *)
%t A202323 RealDigits[ ProductLog[E^3] - 3, 10, 99] // First (* _Jean-François Alcover_, Feb 14 2013 *)
%o A202323 (PARI) lambertw(exp(3)) - 3 \\ _G. C. Greubel_, Jun 10 2017
%Y A202323 Cf. A202322.
%K A202323 nonn,cons
%O A202323 0,1
%A A202323 _Clark Kimberling_, Dec 18 2011
%E A202323 a(97)-a(98) corrected by _Jean-François Alcover_, Feb 14 2013