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A202325 Decimal expansion of x > 0 satisfying x + 3 = exp(x).

%I A202325 #15 Feb 07 2025 16:44:07
%S A202325 1,5,0,5,2,4,1,4,9,5,7,9,2,8,8,3,3,6,6,9,9,8,6,2,4,4,3,2,1,3,7,3,5,3,
%T A202325 9,4,0,0,7,6,8,4,3,5,6,0,1,9,0,2,1,9,8,1,1,6,4,3,7,9,4,4,0,9,2,4,6,7,
%U A202325 9,9,9,0,3,9,9,2,5,4,5,0,8,0,7,1,7,4,7,1,0,9,0,4,4,2,2,2,2,7,4
%N A202325 Decimal expansion of x > 0 satisfying x + 3 = exp(x).
%C A202325 See A202320 for a guide to related sequences. The Mathematica program includes a graph.
%H A202325 G. C. Greubel, <a href="/A202325/b202325.txt">Table of n, a(n) for n = 1..10000</a>
%H A202325 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A202325 x < 0:  -2.9475309025422851275901263887139816414...
%e A202325 x > 0:  1.50524149579288336699862443213735394007...
%t A202325 u = 1; v = 3;
%t A202325 f[x_] := u*x + v; g[x_] := E^x
%t A202325 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A202325 r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
%t A202325 RealDigits[r]  (* A202324 *)
%t A202325 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A202325 RealDigits[r]  (* A202325 *)
%t A202325 RealDigits[-3 - LambertW[-1, -Exp[-3]], 10, 100][[1]] (* _G. C. Greubel_, Nov 09 2017 *)
%o A202325 (PARI) solve(x=0, 2, x+3-exp(x)) \\ _Michel Marcus_, Nov 09 2017
%Y A202325 Cf. A202320.
%K A202325 nonn,cons
%O A202325 1,2
%A A202325 _Clark Kimberling_, Dec 16 2011