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%I #17 Nov 20 2024 23:34:32
%S 1,2,8,9,7,6,1,4,2,5,2,9,2,0,8,3,0,2,1,5,1,1,3,0,6,7,4,1,2,7,7,4,8,2,
%T 8,9,8,5,7,5,4,6,7,1,9,7,0,8,8,3,9,9,6,9,3,0,1,1,9,8,0,2,2,1,5,1,1,4,
%U 6,1,1,3,4,1,8,3,7,3,2,7,2,5,2,1,4,0,1,8,0,1,8,6,0,5,3,5,3,0,9,1
%N Decimal expansion of arctan(sqrt(12)).
%H G. C. Greubel, <a href="/A195724/b195724.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 arcsin(sqrt(12/13)) = arccos(sqrt(1/13)). - _Amiram Eldar_, Jul 04 2023
%e 1.289761425292083021511306741277...
%t r = Sqrt[12]; N[ArcTan[r], 100]
%t RealDigits[%] (* A195724 *)
%t RealDigits[ArcTan[2*Sqrt[3]], 10, 100][[1]] (* _G. C. Greubel_, Aug 20 2018 *)
%o (PARI) atan(2*sqrt(3)) \\ _G. C. Greubel_, Aug 20 2018
%o (Magma) SetDefaultRealField(RealField(100)); Arctan(2*Sqrt(3)); // _G. C. Greubel_, Aug 20 2018
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Sep 23 2011