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Search: id:A156020
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| A156020 |
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Denominators in an infinite sum for Pi |
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+0
4
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| 1, 106, 877203, 2195225334, 17599271777, 360950005720, 17348726394920, 1996375977735378, 26627865341803449, 668044491303666717, 13157161331655387213, 7653283960850915182425, 3256741424583567733172850
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OFFSET
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2,2
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COMMENT
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Pi = 3/1 + 15/106 + 73/877203 + 1/2195225334 + 2/17599271777 +
3/360950005720 + 7/17348726394920 + ... +
Sum of first 4 terms = 3.14159265347...; where Pi = 3.14159265359... f
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FORMULA
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Given the convergents of Pi <Pi, A002485(2k)/A002486(2k), k>1, = Q(2k); Pi = 3/1 + SUM_{k..inf.}: (Q(2*(k+1) - Q(2*k))
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EXAMPLE
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a(2) = 106 since A002485(4)/A002486(4) - A002485(2)/A002486(2) = 333/106 -
3/1 = 15/106
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CROSSREFS
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Cf. A002485, A002486, A156019
Sequence in context: A166912 A078281 A082177 this_sequence A160487 A096712 A161176
Adjacent sequences: A156017 A156018 A156019 this_sequence A156021 A156022 A156023
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), Feb 01 2009
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EXTENSIONS
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Added more terms Alexander R. Povolotsky (pevnev(AT)juno.com), Sep 01 2009
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