A195729 - OEIS

%I #18 Nov 20 2024 23:48:42

%S 1,2,4,9,0,4,5,7,7,2,3,9,8,2,5,4,4,2,5,8,2,9,9,1,7,0,7,7,2,8,1,0,9,0,

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

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

%N Decimal expansion of arctan(3).

%H G. C. Greubel, <a href="/A195729/b195729.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals arctan(1) + arctan(1/2). - _Charles R Greathouse IV_, Sep 23 2014

%F Equals arcsin(3/sqrt(10)) = arccos(sqrt(1/10)). - _Amiram Eldar_, Jul 11 2023

%e arctan(3) = 1.2490457723982544258299170772...

%t r = 3;

%t N[ArcTan[r], 100]

%t RealDigits[%]  (* A195729 *)

%t N[ArcCot[r], 100]

%t RealDigits[%]  (* A105531 *)

%t N[ArcSec[r], 100]

%t RealDigits[%]  (* A137914 *)

%t N[ArcCsc[r], 100]

%t RealDigits[%]  (* A188615 *)

%o (PARI) atan(3) \\ _Charles R Greathouse IV_, Sep 23 2014

%o (Magma) SetDefaultRealField(RealField(100)); Arctan(3); // _G. C. Greubel_, Aug 20 2018

%Y Cf. A105531, A137914, A188615.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Sep 23 2011