OFFSET
1,2
COMMENTS
r(n) = tan(2^(n-1)*arctan(1/A024810(n))) is always a rational number such that its limit lim_{n->oo} r(n)=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.
FORMULA
a(n) = denominator(tan(2^(n-1)*arctan(1/A024810(n)))).
MATHEMATICA
a[n_] := Module[{}, z[n] = (Floor[2^(n + 1)/\[Pi]] + I)^2^(n - 1); Denominator[Im[z[n]]/Re[z[n]]]];
Print[a[1], " ", a[2], " ", a[3], " ", a[4], " ", a[5], " ", a[6]];
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Sanjar Abrarov, Sep 03 2024
STATUS
approved