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_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 06 2011
proposed
approved
editing
proposed
allocated for Clark KimberlingDecimal expansion of the number x satisfying x^2+3x+5=e^x.
3, 2, 2, 0, 0, 1, 7, 9, 5, 0, 5, 2, 5, 7, 1, 0, 2, 9, 5, 7, 7, 7, 0, 9, 2, 0, 9, 2, 5, 0, 5, 1, 3, 0, 1, 7, 8, 3, 9, 2, 9, 8, 3, 1, 6, 0, 4, 3, 3, 1, 1, 5, 5, 0, 8, 4, 6, 2, 9, 1, 1, 4, 0, 0, 9, 8, 2, 4, 9, 0, 5, 6, 5, 5, 3, 2, 3, 7, 6, 0, 7, 0, 3, 7, 7, 3, 6, 5, 3, 1, 3, 0, 2, 0, 7, 8, 8, 9, 8
1,1
See A201741 for a guide to related sequences. The Mathematica program includes a graph.
x=3.220017950525710295777092092505130178392983...
a = 1; b = 3; c = 5;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 3.3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
RealDigits[r] (* A201902 *)
Cf. A201741.
allocated
nonn,cons
Clark Kimberling (ck6(AT)evansville.edu), Dec 06 2011
approved
editing
allocated for Clark Kimberling
allocated
approved