cp's OEIS Frontend

A201767 Decimal expansion of the least x satisfying 10 - x^2 = e^x.

%I A201767 #10 Feb 07 2025 16:44:07
%S A201767 3,1,5,5,5,3,2,3,3,0,7,9,6,3,4,6,4,4,6,9,3,2,3,0,3,3,1,9,2,6,5,8,4,0,
%T A201767 7,0,0,0,1,0,4,2,5,6,4,4,8,9,1,1,1,9,8,6,3,7,4,6,9,1,3,5,4,3,7,9,8,7,
%U A201767 6,6,6,9,4,4,2,6,5,5,6,4,0,3,8,8,5,0,7,3,6,1,5,0,4,4,1,0,2,2,6
%N A201767 Decimal expansion of the least x satisfying 10 - x^2 = e^x.
%C A201767 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201767 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201767 least:  -3.1555323307963464469323033192658407000...
%e A201767 greatest:  1.87144644984680656529114045650417237...
%t A201767 a = -1; b = 0; c = 10;
%t A201767 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201767 Plot[{f[x], g[x]}, {x, -4, 3}, {AxesOrigin -> {0, 0}}]
%t A201767 r = x /. FindRoot[f[x] == g[x], {x, -3.2, -3.1}, WorkingPrecision -> 110]
%t A201767 RealDigits[r]     (* A201767 *)
%t A201767 r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]
%t A201767 RealDigits[r]    (* A201768 *)
%Y A201767 Cf. A201741.
%K A201767 nonn,cons
%O A201767 1,1
%A A201767 _Clark Kimberling_, Dec 05 2011
%E A201767 a(93) onwards corrected by _Georg Fischer_, Aug 03 2021