A135459 Numbers n such that the difference between sqrt(2)*n and the nearest integer is smaller than 1/10.

5, 12, 17, 24, 29, 34, 36, 41, 46, 53, 58, 63, 65, 70, 75, 82, 87, 94, 99, 104, 106, 111, 116, 123, 128, 133, 135, 140, 145, 152, 157, 164, 169, 174, 176, 181, 186, 193, 198, 203, 205, 210, 215, 222, 227, 232, 234, 239, 244, 251, 256, 263, 268, 273, 275, 280

Offset

1,1

Comments

The equidistribution theorem states that n*sqrt(2) is equidistributed modulo 1, therefore lim_{n->infinity} a(n)/n = 5.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

24 is in the list because sqrt(2)*24 = 33.94 which is within 0.1 of an integer.

Maple

filter:= proc(n) local m;
 m:= floor(n*sqrt(2));
   2*n^2 < (m+1/10)^2 or 2*n^2 > (m+9/10)^2
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 14 2016

Mathematica

Select[Range[300], Abs[Sqrt[2]*# - If[Sqrt[2]*# - Floor[Sqrt[2]*# ] < 1/2, Floor[Sqrt[2]*# ], Ceiling[Sqrt[2]*# ]]] < 0.1 &]

Crossrefs

Sequence in context: A089988 A314286 A314287 * A214067 A290494 A246787

Adjacent sequences: A135456 A135457 A135458 * A135460 A135461 A135462

Keyword

nonn

Author

Ben Paul Thurston, Dec 15 2007

Extensions

Edited and extended by Stefan Steinerberger, Dec 16 2007

Status

approved