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A247357
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Least m such that (4/m^2)*Sum_{k=0..m} sqrt(m^2 - k^2) < Pi + 1/n.
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1
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1, 3, 5, 7, 8, 10, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 35, 37, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120
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OFFSET
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1,2
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COMMENTS
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a(n+1) - a(n) is in {1,2} for n >= 1.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 17.
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LINKS
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MATHEMATICA
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z = 200; s[m_] := s[m] = (4/m^2) Sum[Sqrt[m^2 - k^2], {k, 0, m}]
f[n_] := f[n] = Select[Range[z], s[#] < Pi + 1/n &, 1]
u = Flatten[Table[f[n], {n, 1, z}]]
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CROSSREFS
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easy
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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