A375935 Denominator of rational number tan(2^(n-1)*arctan(1/A024810(n))).

1, 3, 119, 72697201, 466125047039779152001, 1298332088620573402611989909424448036756809624806401

Offset: 1

Author

Sanjar Abrarov, Sep 03 2024

Keywords

• nonn
• frac

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.

Crossrefs

Cf. A024810, A374723 (numerators).

Programs

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]];

Formula

a(n) = denominator(tan(2^(n-1)*arctan(1/A024810(n)))).