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A293324 The integer k that minimizes |k/2^n - 1/tau|, where tau = (1+sqrt(5))/2 = golden ratio.

%I A293324 #4 Oct 09 2017 08:25:25
%S A293324 1,1,2,5,10,20,40,79,158,316,633,1266,2531,5063,10126,20252,40503,
%T A293324 81007,162014,324028,648056,1296111,2592222,5184445,10368890,20737779,
%U A293324 41475559,82951118,165902236,331804471,663608942,1327217885,2654435769,5308871539
%N A293324 The integer k that minimizes |k/2^n - 1/tau|, where tau = (1+sqrt(5))/2 = golden ratio.
%H A293324 Clark Kimberling, <a href="/A293324/b293324.txt">Table of n, a(n) for n = 0..1000</a>
%F A293324 a(n) = floor(1/2 + r*2^n), where r = (-1+sqrt(5))/2.
%F A293324 a(n) = A293322(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293323(n).
%t A293324 z = 120; r = -1+GoldenRatio;
%t A293324 Table[Floor[r*2^n], {n, 0, z}];   (* A293322 *)
%t A293324 Table[Ceiling[r*2^n], {n, 0, z}]; (* A293323 *)
%t A293324 Table[Round[r*2^n], {n, 0, z}];   (* A293324 *)
%Y A293324 Cf. A001622, A293322, A293323.
%K A293324 nonn,easy
%O A293324 0,3
%A A293324 _Clark Kimberling_, Oct 07 2017