A201906 Decimal expansion of the x nearest 0 that satisfies x^2 + 4*x + 2 = e^x.

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

Offset: 0

Author

Clark Kimberling, Dec 06 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least:  -3.425667410202877373265626064725816697827357...
nearest to 0:  -0.35687491913863648565066705875991244...
greatest:  3.2349232177760663670327961327304430448478...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 4; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 3.3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.5, -3.4}, WorkingPrecision -> 110]
RealDigits[r]     (* A201905 *)
r = x /. FindRoot[f[x] == g[x], {x, -.36, -.35}, WorkingPrecision -> 110]
RealDigits[r]     (* A201906 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
RealDigits[r]     (* A201907 *)

Extensions

a(84) onwards corrected by Georg Fischer, Aug 03 2021