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%I #13 Oct 14 2016 14:59:04
%S 5,12,17,24,29,34,36,41,46,53,58,63,65,70,75,82,87,94,99,104,106,111,
%T 116,123,128,133,135,140,145,152,157,164,169,174,176,181,186,193,198,
%U 203,205,210,215,222,227,232,234,239,244,251,256,263,268,273,275,280
%N Numbers n such that the difference between sqrt(2)*n and the nearest integer is smaller than 1/10.
%C The equidistribution theorem states that n*sqrt(2) is equidistributed modulo 1, therefore lim_{n->infinity} a(n)/n = 5.
%H G. C. Greubel, <a href="/A135459/b135459.txt">Table of n, a(n) for n = 1..1000</a>
%e 24 is in the list because sqrt(2)*24 = 33.94 which is within 0.1 of an integer.
%p filter:= proc(n) local m;
%p m:= floor(n*sqrt(2));
%p 2*n^2 < (m+1/10)^2 or 2*n^2 > (m+9/10)^2
%p end proc:
%p select(filter, [$1..1000]); # _Robert Israel_, Oct 14 2016
%t Select[Range[300], Abs[Sqrt[2]*# - If[Sqrt[2]*# - Floor[Sqrt[2]*# ] < 1/2, Floor[Sqrt[2]*# ], Ceiling[Sqrt[2]*# ]]] < 0.1 &]
%K nonn
%O 1,1
%A _Ben Paul Thurston_, Dec 15 2007
%E Edited and extended by _Stefan Steinerberger_, Dec 16 2007
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