login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)