A196618 Decimal expansion of cos(x), where x is the least positive solution of 1 = (x^2)*cos(x).

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

Offset: 0

Author

Clark Kimberling, Oct 05 2011

Keywords

• nonn
• cons

Examples

			x = 0.4816817785482382699874297227751696380614905...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A196617, A196619.

Programs

Mathematica

Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
RealDigits[xt]      (* A196617 *)
Cos[xt]
RealDigits[Cos[xt]] (* A196618 *)
c = N[1/xt - Cos[xt], 100]
RealDigits[c]       (* A196619 *)
slope = -Sin[xt]
RealDigits[slope]   (* A196620 *)

PARI

a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); cos(x) \\ G. C. Greubel, Aug 22 2018

Extensions

Terms a(85) onward corrected by G. C. Greubel, Aug 22 2018