A201933 Decimal expansion of the least x satisfying x^2 + 5*x + 2 = e^x.

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

Offset: 1

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:  -4.5640783603793772013414868523420...
nearest to 0:  -0.259069533051109108686405...
greatest:  3.43200871161068035280379146269...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 5; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -4.6, -4.5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201933 *)
r = x /. FindRoot[f[x] == g[x], {x, -.3, -.2}, WorkingPrecision -> 110]
RealDigits[r]     (* A201934 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201935 *)

Extensions

a(87) onwards corrected by Georg Fischer, Aug 03 2021