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Search: id:A091930
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| A091930 |
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Write pi = Sum_{n >= 1} 1/sqrt(a(n)), where each a(n) is minimal, unique and the sum approaches pi from below. |
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1
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| 1, 2, 3, 4, 8, 77929, 17700337092966627, 97049570583433629023486339792437254323980677153951, 5843929411147236787850533935034401259024361461871518737494060444501523486808548249023180720047062910088805381472125716317734317997138497838459864230713
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first eight terms give Pi accurately to the first 75 decimal digits.
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FORMULA
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a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4; a(n) = ceiling((pi - Sum_{i=1..n-1}(1/sqrt(a(i))))^-2).
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EXAMPLE
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pi > 1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4) + 1/sqrt(8), but pi < 1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4) + 1/sqrt(7).
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MATHEMATICA
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a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 4; a[n_] := Ceiling[(Pi - Sum[1/Sqrt[a[i]], {i, 1, n - 1}])^-2]; Table[ a[n], {n, 1, 9}]
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CROSSREFS
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Sequence in context: A129284 A100997 A128657 this_sequence A124526 A124418 A112480
Adjacent sequences: A091927 A091928 A091929 this_sequence A091931 A091932 A091933
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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), Feb 13 2004
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