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A293322 Greatest integer k such that k/2^n < 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.

%I A293322 #7 Oct 09 2017 08:25:10
%S A293322 0,1,2,4,9,19,39,79,158,316,632,1265,2531,5062,10125,20251,40503,
%T A293322 81006,162013,324027,648055,1296111,2592222,5184444,10368889,20737779,
%U A293322 41475558,82951117,165902235,331804471,663608942,1327217884,2654435769,5308871538
%N A293322 Greatest integer k such that k/2^n < 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.
%H A293322 Clark Kimberling, <a href="/A293322/b293322.txt">Table of n, a(n) for n = 0..1000</a>
%F A293322 a(n) = floor((r*2^n)), where r = (-1+sqrt(5))/2.
%F A293322 a(n) = A293323(n) - 1.
%t A293322 z = 120; r = -1+GoldenRatio;
%t A293322 Table[Floor[r*2^n], {n, 0, z}];   (* A293322 *)
%t A293322 Table[Ceiling[r*2^n], {n, 0, z}]; (* A293323 *)
%t A293322 Table[Round[r*2^n], {n, 0, z}]; (* A293324 *)
%o A293322 (PARI) a(n) = 2^n*(sqrt(5)-1)\2; \\ _Altug Alkan_, Oct 08 2017
%Y A293322 Cf. A001622, A293313, A293323, A293324.
%K A293322 nonn,easy
%O A293322 0,3
%A A293322 _Clark Kimberling_, Oct 07 2017