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We present a new form of the Machin-like formula for $\pi$ that can begenerated by using iteration. This form of the Machin-like formula may bepromising for computation of the constant $\pi$ due to rapidly increasingintegers at each step of the iteration. The computational test we performedshows that, with an integer $k \ge 17$, the Lehmer measure remains small andpractically does not increase after $18$ steps of iteration.

A new form of the Machin-like formula for pi by iteration with increasing integers