This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344906 #28 Nov 15 2024 23:36:13
%S A344906 1,7,4,3,2,8,6,6,2,0,4,7,2,3,4,0,0,0,3,5,0,4,3,3,7,6,5,6,1,3,6,4,1,6,
%T A344906 2,8,5,8,1,3,8,3,1,1,8,5,4,2,8,2,0,6,5,2,3,0,0,4,5,6,9,5,7,2,0,5,6,5,
%U A344906 5,1,7,6,5,2,2,7,4,9,2,0,5,5,8,1,6,5,8,6,8
%N A344906 Decimal expansion of Sum_{k>=0} arctan(1/2^k).
%C A344906 This number can be interpreted geometrically as the angle in radians of a fan made of stacked right triangles, with the length to height ratio doubling each successive triangle as seen in the illustration.
%C A344906 Since this angle exceeds Pi/2, the set of rotation angles used in the CORDIC algorithm covers an angle range sufficient to compute sine and cosine for any angle between 0 and Pi/2. This means the algorithm can converge to any angle in that range through appropriate combinations of these basic rotations. - _Daniel Hoyt_, Oct 25 2024
%H A344906 Daniel Hoyt, <a href="/A344906/a344906.png">Illustration of this angle's arctan relationship</a>.
%H A344906 Wikipedia, <a href="https://en.wikipedia.org/wiki/CORDIC#Rotation_mode">CORDIC</a>.
%F A344906 Equals Sum_{k>=1} (-1)^(k+1)*2^(2*k-1)/((2^(2*k-1)-1)*(2*k-1)).
%e A344906 1.743286620472340003...
%p A344906 Digits:= 140:
%p A344906 evalf(sum(arccot(2^k), k=0..infinity)); # _Alois P. Heinz_, Jun 02 2021
%o A344906 (PARI) suminf(k=0, atan(1/2^k))
%o A344906 (PARI) sumalt(k=1, ((-1)^(k+1))*2^(2*k-1)/((2^(2*k-1)-1)*(2*k-1)))
%Y A344906 Cf. A003881, A065445, A073000, A195727, A195782.
%K A344906 nonn,cons
%O A344906 1,2
%A A344906 _Daniel Hoyt_, Jun 01 2021