cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A201746 Decimal expansion of the number x satisfying x^2+7=e^x.

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%I A201746 #10 Jun 11 2025 16:13:13
%S A201746 2,6,3,4,9,8,9,9,1,5,7,5,9,3,4,7,9,1,8,3,9,4,7,4,7,7,4,3,7,3,8,5,9,6,
%T A201746 5,4,3,7,3,6,2,5,4,5,6,0,2,7,0,1,4,0,7,8,9,1,4,4,9,4,6,0,8,3,4,5,9,3,
%U A201746 3,4,7,6,4,5,6,3,8,5,6,6,9,2,3,6,4,4,5,1,8,3,4,9,0,4,9,1,3,2,2
%N A201746 Decimal expansion of the number x satisfying x^2+7=e^x.
%C A201746 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201746 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201746 x=2.634989915759347918394747743738596543736254...
%t A201746 a = 1; b = 0; c = 7;
%t A201746 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201746 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A201746 r = x /. FindRoot[f[x] == g[x], {x, 2.6, 2.7}, WorkingPrecision -> 110]
%t A201746 RealDigits[r]   (* A201746 *)
%t A201746 RealDigits[x/.FindRoot[x^2+7==E^x,{x,2.6},WorkingPrecision->120],10,120][[1]] (* _Harvey P. Dale_, Jun 11 2025 *)
%Y A201746 Cf. A201741.
%K A201746 nonn,cons
%O A201746 1,1
%A A201746 _Clark Kimberling_, Dec 05 2011