A350799 The number of decimal places of Pi that are computed correctly when using Machin's formula with n terms of the Taylor series.

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, 37, 38, 40, 40, 43, 42, 45, 47, 47, 49, 51, 53, 54, 55, 57, 58, 59, 60, 62, 64, 65, 67, 68, 69, 71, 72, 74, 75, 75, 77, 79, 80, 82

Offset

1,2

Comments

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.

Links

Matthew Scroggs, Table of n, a(n) for n = 1..200

Matthew Scroggs, Python code

Wikipedia, John Machin

Example

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.

Crossrefs

Cf. A000796, A096954, A096955.

Sequence in context: A228373 A156271 A186513 * A246438 A158791 A144717

Adjacent sequences: A350796 A350797 A350798 * A350800 A350801 A350802

Keyword

nonn,base

Author

Matthew Scroggs, Jan 18 2022.

Status

approved