OFFSET
1,2
COMMENTS
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.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..66
EXAMPLE
|50*Pi - 157| and |50*e - 136| are both less than 1/sqrt(50) so 50 is in the sequence.
MAPLE
nm:= x -> abs(x-round(x)):
f:= n -> is(max(nm(n*Pi), nm(n*exp(1)))<n^(-1/2)):
select(f, [$1 .. 20000]);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Robert Israel, Feb 27 2012
STATUS
approved