A329960 Decimal expansion of least positive number x such that 1/(2 + sin x) + 1/(2 + cos x) = 1.

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

Offset

1,1

Links

Table of n, a(n) for n=1..86.

Formula

Exact value: x = arccos(-(1/2) + 1/sqrt(2) - 1/2 sqrt(-1 + 2 sqrt(2)))

Example

least positive x:  2.0589431288711381228941594943312845878...

Mathematica

Solve[1/(2 + Sin[x]) + 1/(2 + Cos[x]) == 1, x]
u = ArcCos[-(1/2) + 1/Sqrt[2] - 1/2 Sqrt[-1 + 2 Sqrt[2]]]
u1 = N[u, 150]
RealDigits[u1, 10][[1]]  (* A329960 *)
Plot[1/(2 + Sin[x]) + 1/(2 + Cos[x]) - 1, {x, -1, 3}]

Crossrefs

Cf. A329961, A329962.

Sequence in context: A334059 A133446 A011122 * A085009 A192883 A011435

Adjacent sequences: A329957 A329958 A329959 * A329961 A329962 A329963

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved