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A135459
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Numbers n such that the difference between sqrt(2)*n and the nearest integer is smaller than 1/10.
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1
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5, 12, 17, 24, 29, 34, 36, 41, 46, 53, 58, 63, 65, 70, 75, 82, 87, 94, 99, 104, 106, 111, 116, 123, 128, 133, 135, 140, 145, 152, 157, 164, 169, 174, 176, 181, 186, 193, 198, 203, 205, 210, 215, 222, 227, 232, 234, 239, 244, 251, 256, 263, 268, 273, 275, 280
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OFFSET
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1,1
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COMMENTS
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The equidistribution theorem states that n*sqrt(2) is equidistributed modulo 1, therefore lim_{n->infinity} a(n)/n = 5.
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LINKS
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EXAMPLE
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24 is in the list because sqrt(2)*24 = 33.94 which is within 0.1 of an integer.
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MAPLE
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filter:= proc(n) local m;
m:= floor(n*sqrt(2));
2*n^2 < (m+1/10)^2 or 2*n^2 > (m+9/10)^2
end proc:
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MATHEMATICA
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Select[Range[300], Abs[Sqrt[2]*# - If[Sqrt[2]*# - Floor[Sqrt[2]*# ] < 1/2, Floor[Sqrt[2]*# ], Ceiling[Sqrt[2]*# ]]] < 0.1 &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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