%I #34 Feb 01 2022 09:20:07

%S 1,2,3,5,7,8,9,11,12,14,16,17,18,19,21,22,24,25,27,29,30,30,32,34,36,

%T 37,38,40,40,43,42,45,47,47,49,51,53,54,55,57,58,59,60,62,64,65,67,68,

%U 69,71,72,74,75,75,77,79,80,82

%N The number of decimal places of Pi that are computed correctly when using Machin's formula with n terms of the Taylor series.

%C Machin's formula states that Pi/4 = 4*arctan(1/5) - arctan(1/239). An approximation of Pi can be found by computing this using a Taylor series approximation of arctan. a(n) is the number of decimal places that are correct when n terms are included in the Taylor series approximation.

%H Matthew Scroggs, <a href="/A350799/b350799.txt">Table of n, a(n) for n = 1..200</a>

%H Matthew Scroggs, <a href="https://github.com/mscroggs/machins-formula/blob/main/A350799.py">Python code</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/John_Machin">John Machin</a>

%e For n = 3, Machin's formula with three terms in the Taylor series gives 3.14162102932503442504 as an approximation of Pi. The first 3 decimal places (141) are correct, so a(3) = 3.

%Y Cf. A000796, A096954, A096955.

%K nonn,base

%O 1,2

%A _Matthew Scroggs_, Jan 18 2022.