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A350799
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The number of decimal places of Pi that are computed correctly when using Machin's formula with n terms of the Taylor series.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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