A198822 Decimal expansion of x > 0 satisfying x^2 - 2*cos(x) = 2.

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

Offset: 1

Author

Clark Kimberling, Oct 30 2011

Keywords

• nonn
• cons

Comments

See A198755 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			1.47817026643032128331062417534774680802682351780...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A003957, A198755.

Programs

Mathematica

a = 1; b = -2; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A198822 *)

PARI

solve(x=0,1,cos(x)-x)*2 \\ Gleb Koloskov, Jun 16 2021

Formula

Equals 2*A003957. - Gleb Koloskov, Jun 16 2021