Journal of Integer Sequences, Vol. 25 (2022), Article 22.4.5

A New Form of the Machin-like Formula for π by Iteration with Increasing Integers

Sanjar M. Abrarov, Rehan Siddiqui, and Rajinder K. Jagpal
Epic College of Technology
5670 McAdam Rd.
Mississauga, ON L4Z 1T2

Brendan M. Quine
Department of Physics and Astronomy
York University
4700 Keele St.
Toronto, ON M3J 1P3


We present a new form of the Machin-like formula for π that can be generated by using iteration. This form of the Machin-like formula may be promising for computation of the constant π due to rapidly increasing integers at each step of the iteration. The computational test we performed shows that, with an integer k ≥ 17, the Lehmer measure remains small and practically does not increase after 18 steps of iteration.

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Received November 25 2021; revised versions received March 28 2022; March 31 2022; April 2 2022; April 10 2022. Published in Journal of Integer Sequences, April 10 2022.

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