Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #12 Jan 16 2025 02:38:01
%S 0,0,0,0,0,0,0,0,0,5,2,0,2,5,2,4,1,8,4,7,0,6,4,5,0,4,8,0,4,8,9,8,9,9,
%T 4,6,7,5,0,7,6,0,1,4,6,7,8,7,4,8,4,4,5,1,2,2,9,2,6,5,2,2,5,9,7,0,0,3,
%U 1,3,7,0,0,2,5,4,0,0,5,5,8,0,4,6,9,6,0,7,7,7,5,3,4,6,7,7,6,6,1,2,5,0,4,8
%N Decimal expansion of K210.
%C Related to modular functions and approximations to Pi: K210 is one of the most famous singular value calculated by Ramanujan. -2/sqrt(210)*log(K210/4) = 3.14159265358979323847198... agrees with Pi to 20 decimal places.
%D Lennart Berggren, Jonathan Borwein, and Peter Borwein, Pi a source Book, second edition, Springer, 2000, p. 592.
%F K210 = (sqrt(2)-1)^2*(2-sqrt(3))*(sqrt(7)-sqrt(6))^2*(8-3*sqrt(7))*(sqrt(10)-3)^2*(sqrt(15)-sqrt(14))*(4-sqrt(15))^2*(6-sqrt(35)).
%e 0.0000000005202524184706450480489....
%t RealDigits[(Sqrt[2]-1)^2 * (2-Sqrt[3])*(Sqrt[7]-Sqrt[6])^2 * (8-3*Sqrt[7]) * (Sqrt[10]-3)^2 * (Sqrt[15]-Sqrt[14]) * (4-Sqrt[15])^2 * (6-Sqrt[35]), 10, 120, -1][[1]] (* _Amiram Eldar_, Jan 16 2025 *)
%K cons,nonn,changed
%O 0,10
%A _Benoit Cloitre_, Dec 03 2002