A195707 Decimal expansion of arctan(sqrt(5/8)).

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

Offset: 0

Author

Clark Kimberling, Sep 23 2011

Keywords

• nonn
• cons

Examples

			arctan(sqrt(5/8)) = 0.6689640742...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers

Crossrefs

Cf. A195700, A195703, A195711.

Programs

Magma

SetDefaultRealField(RealField(100)); Arctan(Sqrt(5/8)); // G. C. Greubel, Aug 19 2018

Mathematica

r = Sqrt[5/8];
N[ArcSin[r], 100]
RealDigits[%]  (* A195703 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A195700 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A195707 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A195711 *)

PARI

atan(sqrt(5/8)) \\ G. C. Greubel, Aug 19 2018

Formula

Equals arcsin(sqrt(5/13)) = arccos(2*sqrt(2/13)). - Amiram Eldar, Jul 08 2023