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A208530
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Numbers n such that both n*Pi and n*e are within 1/sqrt(n) of integers.
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2
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1, 2, 3, 4, 5, 6, 7, 8, 14, 15, 21, 22, 28, 29, 35, 36, 43, 50, 57, 64, 71, 78, 85, 92, 671, 678, 685, 1356, 1363, 2034, 2041, 2719, 3397, 4075, 4753, 5431, 18412, 19090, 19768
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OFFSET
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1,2
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COMMENTS
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For any irrational x and y there exist infinitely many positive integers n such that max(|n*x - Z|,|n*y - Z|)) < 1/sqrt(n), where Z is the set of integers.
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LINKS
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EXAMPLE
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|50*Pi - 157| and |50*e - 136| are both less than 1/sqrt(50) so 50 is in the sequence.
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MAPLE
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nm:= x -> abs(x-round(x)):
f:= n -> is(max(nm(n*Pi), nm(n*exp(1)))<n^(-1/2)):
select(f, [$1 .. 20000]);
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MATHEMATICA
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fQ[n_] := Abs[n*Pi - Round[n*Pi]] < 1/Sqrt[n] && Abs[n*E - Round[n*E]] < 1/Sqrt[n]; Select[Range@ 20000, fQ@# &] (* Robert G. Wilson v, Mar 10 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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