A140244 Decimal expansion of arccos(-1/4).

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

Offset

1,2

Comments

Angle in radians of the obtuse angle of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths.

A140240 + A140242 + A140244 = arccos(7/8) + arccos(11/16) + arccos(-1/4) = Pi.

Arccos(-1/4) is the least positive x for which the function f(x)=cos(x)+cos(2x) attains its minimum value, which is -9/8. - Clark Kimberling, Oct 28 2011

Links

Table of n, a(n) for n=1..105.

Formula

arccos(-1/4) = Pi - arcsin(sqrt(15)/4) = Pi - arctan(sqrt(15)).

Example

1.82347658193697527271697912863346241435077843278439110412139607489448326362...

Mathematica

RealDigits[ArcCos[-1/4], 10, 120][[1]] (* Harvey P. Dale, Dec 20 2016 *)

Prog

(PARI) acos(-1/4)

Crossrefs

Cf. A140239, A140240, A140241, A140242, A140243, A140245, A140246, A140247, A140248, A140249.

Sequence in context: A291362 A319090 A222225 * A160105 A167162 A307154

Adjacent sequences: A140241 A140242 A140243 * A140245 A140246 A140247

Keyword

cons,nonn

Author

Rick L. Shepherd, May 14 2008

Status

approved