_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 06 2011

proposed

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editing

proposed

allocated for Clark KimberlingDecimal expansion of the least x satisfying x^2+4x+3=e^x.

3, 0, 2, 4, 0, 1, 4, 5, 0, 1, 1, 3, 5, 2, 9, 3, 7, 8, 4, 7, 7, 5, 5, 8, 9, 6, 2, 7, 7, 9, 7, 3, 9, 5, 3, 5, 1, 6, 5, 9, 8, 2, 8, 2, 8, 7, 1, 3, 2, 9, 0, 7, 9, 1, 9, 8, 7, 5, 0, 3, 5, 5, 4, 8, 2, 6, 2, 3, 8, 2, 5, 2, 4, 7, 0, 6, 6, 4, 3, 2, 9, 4, 3, 2, 4, 8, 4, 3, 4, 2, 4, 1, 0, 3, 3, 5, 6, 4, 2

1,1

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

least: -3.024014501135293784775589627797395351659...

nearest to 0: -0.79522661386054079889626155638871...

greatest: 3.2986275628038651802559413164923413431...

a = 1; b = 4; c = 3;

f[x_] := a*x^2 + b*x + c; g[x_] := E^x

Plot[{f[x], g[x]}, {x, -3.5, 3.5}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]

RealDigits[r] (* A201924 *)

r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]

RealDigits[r] (* A201925 *)

r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]

RealDigits[r] (* A201926 *)

Cf. A201741.

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Clark Kimberling (ck6(AT)evansville.edu), Dec 06 2011

approved

editing

allocating

allocated

allocated for Clark Kimberling

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