A196773 Decimal expansion of the least number x>0 satisfying -1=(x^2)*cos(x).

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

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Example

x=1.863045308248699224069793204693635418...

Mathematica

Plot[{1/x + .42, Sin[x]}, {x, 0, 2 Pi}]
t = x /. FindRoot[-1 == (x^2) Cos[x], {x, 1.5, 2.5}, WorkingPrecision -> 100]
RealDigits[t]    (* A196773 *)
c = N[-1/t + Sin[t], 100]
RealDigits[c]    (* A196774 *)
slope = N[-1/t^2, 100]
RealDigits[slope](* A196775 *)
RealDigits[x/.FindRoot[x^2 Cos[x]+1, {x, 1/4}, WorkingPrecision->120], 10, 120][[1]] (* Harvey P. Dale, Dec 14 2023 *)

Crossrefs

Cf. A196774.

Sequence in context: A323810 A342946 A195336 * A197824 A085666 A084895

Adjacent sequences: A196770 A196771 A196772 * A196774 A196775 A196776

Keyword

nonn,cons

Author

Clark Kimberling, Oct 06 2011

Status

approved