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Decimal expansion of arctan(1/7).
2

%I #30 Jul 11 2023 03:37:23

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

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

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

%N Decimal expansion of arctan(1/7).

%H D. H. Lehmer, <a href="https://www.maa.org/sites/default/files/pdf/pubs/amm_supplements/Monthly_Reference_7.pdf">On Arccotangent Relations for π</a>, The American Mathematical Monthly, Vol. 45, No. 10 (Dec., 1938), pp. 657-664.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Machin-LikeFormulas.html">Machin-Like Formulas</a>.

%F 2*A073000 - arctan(1/7) = 2*A105531 + arctan(1/7) = Pi/4.

%F 5*arctan(1/7) + 2*arctan(3/79) = Pi/4. - _Frank Ellermann_, Mar 01 2020

%F Equals arcsin(1/(5*sqrt(2))) = arccos(7/(5*sqrt(2))). - _Amiram Eldar_, Jul 11 2023

%e 0.1418970546041639228128516171...

%t RealDigits[ArcTan[1/7],10,120][[1]] (* _Harvey P. Dale_, Oct 03 2012 *)

%o (PARI) atan(1/7) \\ _Michel Marcus_, Mar 01 2020

%Y Cf. A073000, A105531.

%K cons,nonn

%O 0,2

%A Bryan Jacobs (bryanjj(AT)gmail.com), Apr 12 2005