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A293329 The integer k that minimizes |k/2^n - sqrt(1/3)|.

%I A293329 #6 Dec 11 2023 10:45:16
%S A293329 1,1,2,5,9,18,37,74,148,296,591,1182,2365,4730,9459,18919,37837,75674,
%T A293329 151349,302698,605396,1210791,2421583,4843165,9686330,19372660,
%U A293329 38745321,77490641,154981283,309962566,619925131,1239850262,2479700525,4959401049,9918802098
%N A293329 The integer k that minimizes |k/2^n - sqrt(1/3)|.
%H A293329 Clark Kimberling, <a href="/A293329/b293329.txt">Table of n, a(n) for n = 0..1000</a>
%F A293329 a(n) = floor(1/2 + r*2^n), where r = sqrt(1/3).
%F A293329 a(n) = A293327(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293328(n).
%t A293329 z = 120; r = Sqrt[1/3];
%t A293329 Table[Floor[r*2^n], {n, 0, z}];   (* A293327 *)
%t A293329 Table[Ceiling[r*2^n], {n, 0, z}]; (* A293328 *)
%t A293329 Table[Round[r*2^n], {n, 0, z}]; (* A293329 *)
%Y A293329 Cf. A002194, A094386, A293327, A293328.
%K A293329 nonn,easy
%O A293329 0,3
%A A293329 _Clark Kimberling_, Oct 10 2017