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

Author

Clark Kimberling, Sep 23 2011

Keywords

• nonn
• cons

Examples

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

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.
• Index entries for transcendental numbers

Crossrefs

Cf. A188595, A195721, A195722.

Programs

Magma

[Arccos(Sqrt(1/6))]; // G. C. Greubel, Nov 23 2017

Mathematica

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

PARI

atan(sqrt(5)) \\ Michel Marcus, Mar 29 2016

Formula

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