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

%I

%S 1,1,2,5,9,18,37,74,148,296,591,1182,2365,4730,9459,18919,37837,75674,

%T 151349,302698,605396,1210791,2421583,4843165,9686330,19372660,

%U 38745321,77490641,154981283,309962566,619925131,1239850262,2479700525,4959401049,9918802098

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

%H Clark Kimberling, <a href="/A293329/b293329.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(1/2 + r*2^n), where r = sqrt(1/3).

%F a(n) = A293327(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293328(n).

%t z = 120; r = Sqrt[1/3];

%t Table[Floor[r*2^n], {n, 0, z}]; (* A293327 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293328 *)

%t Table[Round[r*2^n], {n, 0, z}]; (* A293329 *)

%Y Cf. A002194, A094386, A293327, A293328.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 10 2017

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)