A201932 Decimal expansion of the greatest x satisfying x^2+5x+1=e^x.

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

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:  -4.79309545512749358956562110850420...
greatest:  3.377361484197400579255025058889...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 5; c = 1;
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, -4.8, -4.7}, WorkingPrecision -> 110]
RealDigits[r]     (* A201931 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.3, 3.4}, WorkingPrecision -> 110]
RealDigits[r]     (* A201932 *)