

A208530


Numbers n such that both n*Pi and n*e are within 1/sqrt(n) of integers.


2



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

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(xround(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

Sequence in context: A032870 A023763 A032904 * A088416 A057913 A245802
Adjacent sequences: A208527 A208528 A208529 * A208531 A208532 A208533


KEYWORD

nonn


AUTHOR

Robert Israel, Feb 27 2012


STATUS

approved



