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Search: id:A105790
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| A105790 |
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Number of bisections to an inscribed triangle to approximate Pi (A000796) to n decimal digits of accuracy. |
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+0
1
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| 1, 4, 4, 6, 8, 9, 11, 13, 14, 16, 17, 19, 21, 23, 25, 26, 27, 30, 31, 33, 34, 36, 38, 40, 41, 43, 45, 46, 47, 49, 53, 53, 54, 56, 58, 60, 61, 62, 65, 66, 67, 70, 71, 72, 75, 76, 78, 80, 83, 83, 84, 87, 89, 89, 91, 93, 94, 96, 98, 99, 100, 103, 105, 107, 107, 109, 112, 112
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Howard Anton, Irl C. Bivens and Stephen L. Davis, Calculus, Early Transcendentals, 7th Edition, John Wiley & Sons, Inc., NY, Section 6.1 An Overview of the Area Problem, page 372-377.
William Dunham, The Calculus Gallery, Masterpieces from Newton to Lebesgue, Princeton University Press, Princeton, NJ 2005, page 56-57.
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FORMULA
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a(n) = 3*2^n*sqrt(2- sqrt(2+ sqrt(2+ ... sqrt(2+ sqrt(3))...))).
A(n) in Table 6.1.1 = Sin( 2Pi/n )*n/2. - Anton.
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MATHEMATICA
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$MaxExtraPrecision =128; p=RealDigits[ Pi, 10, 100][[1]]; f[n_] := 3*2^(n)*Sqrt[2 - Nest[ Sqrt[2 + # ] &, Sqrt[3], n - 1]]; g[n_] := Block[{k = 1, q = Take[p, n + 1]}, While[ Take[ RealDigits[ f[k], 10, 100][[1]], n + 1] != q, k++ ]; k]; Table[ g[n], {n, 69}]
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CROSSREFS
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Cf. A000796.
Sequence in context: A065677 A006672 A107287 this_sequence A090682 A011982 A053639
Adjacent sequences: A105787 A105788 A105789 this_sequence A105791 A105792 A105793
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 20 2005
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