A374723 Numerator of rational number tan(2^(n-1)*arctan(1/A024810(n))).
1, 4, 120, 74455920, 479301523749226879680, 1336367227479573478314645756081634359006026455038720
Offset: 1
Links
- Sanjar M. Abrarov, Rajinder K. Jagpal, Rehan Siddiqui, and Brendan M. Quine, An Iterative Method for Computing π by Argument Reduction of the Tangent Function, Math. Comput. Appl. 2024, 29(2), 17.
Programs
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Mathematica
a[0] := 0; a[n_] := Sqrt[2 + a[n - 1]]; b[n_] := Floor[a[n]/Sqrt[2 - a[n - 1]]]; r[0, x_] := 1; r[1, x_] := (2*x)/(1 - x^2); r[n_, x_] := (2*r[n - 1, x])/(1 - r[n - 1, x]^2); k = 1; While[k <= 6, Print[k, " ", Numerator[r[k - 1, 1/b[k]]]]; k++];
Formula
a(n) = numerator(tan(2^(n-1)*arctan(1/A024810(n)))).
Comments