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A156019
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Numerators in an infinite sum for Pi.
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2
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3, 15, 73, 1, 2, 3, 7, 1, 2, 2, 1, 2, 1, 3, 1, 2, 6, 1, 1, 3, 1, 6, 1, 1, 3, 1, 1, 3, 1, 3, 1, 1, 2, 6, 1, 2, 3, 1, 1, 1, 45, 22, 2, 1, 1, 24, 2, 1, 2, 1, 2, 4, 2, 8, 5, 1, 1, 1, 2, 7, 1, 3, 1, 7, 4, 7, 3, 3, 9, 9, 1, 18, 3, 15, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1
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OFFSET
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1,1
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COMMENTS
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For k >= 0, define Q(k) = A002485(2k)/A002486(2k) (convergents to Pi that are less than Pi), so Pi = Sum_{k>=1} (Q(k) - Q(k-1)). Then a(n) is the numerator of Q(n) - Q(n-1).
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LINKS
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FORMULA
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EXAMPLE
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Pi = 3/1 + 15/106 + 73/877203 + 1/2195225334 + 2/17599271777 + 3/360950005720 + 7/17348726394920 + ....
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- ------------------------------ ------------- ----
0 0/1 = 0 - -
1 3/1 = 3 3/1 3
2 333/106 = 3.1415094339... 15/106 15
3 103993/33102 = 3.1415926530... 73/877203 73
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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