%I
%S 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,
%T 678,685,1356,1363,2034,2041,2719,3397,4075,4753,5431,18412,19090,
%U 19768
%N Numbers n such that both n*Pi and n*e are within 1/sqrt(n) of integers.
%C 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.
%H Robert G. Wilson v, <a href="/A208530/b208530.txt">Table of n, a(n) for n = 1..66</a>
%e 50*Pi  157 and 50*e  136 are both less than 1/sqrt(50) so 50 is in the sequence.
%p nm:= x > abs(xround(x)):
%p f:= n > is(max(nm(n*Pi),nm(n*exp(1)))<n^(1/2)):
%p select(f, [$1 .. 20000]);
%t 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 *)
%K nonn
%O 1,2
%A _Robert Israel_, Feb 27 2012
