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 Israel and Robert G. Wilson v, Table of n, a(n) for n = 1..78
EXAMPLE
|52*log(2) - 41| and |52*log(3) - 65| are both less than 1/sqrt(52) so 52 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*Log[2] - Round[n*Log[2]]] Sqrt[n] < 1 && Abs[n*Log[3] - Round[n*Log[3]]] Sqrt[n] < 1; Select[ Range@ 400000, fQ@ # &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel and Robert G. Wilson v, Jun 28 2015
STATUS
approved