A195720 Decimal expansion of arccos(sqrt(1/6)) and of arcsin(sqrt(5/6)) and arctan(sqrt(5)).

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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Kunle Adegoke, Infinite arctangent sums involving Fibonacci and Lucas numbers, arXiv:1603.08097 [math.NT], 2016.

Formula

Equals Sum_{k >= 1} sqrt(5)/L(2n) where L=A000032. See also A005248. - Michel Marcus, Mar 29 2016

Example

arccos(sqrt(1/6)) = 1.150261991510931...

Mathematica

r = Sqrt[1/6]; RealDigits[ArcCos[r], 10, 100][[1]]

Prog

(PARI) atan(sqrt(5)) \\ Michel Marcus, Mar 29 2016
(Magma) [Arccos(Sqrt(1/6))]; // G. C. Greubel, Nov 23 2017

Crossrefs

Cf. A188595, A195721, A195722.

Sequence in context: A021203 A276712 A199387 * A198883 A261850 A077496

Adjacent sequences: A195717 A195718 A195719 * A195721 A195722 A195723

Keyword

nonn,cons

Author

Clark Kimberling, Sep 23 2011

Status

approved