%I #7 Oct 09 2017 08:25:10

%S 0,1,2,4,9,19,39,79,158,316,632,1265,2531,5062,10125,20251,40503,

%T 81006,162013,324027,648055,1296111,2592222,5184444,10368889,20737779,

%U 41475558,82951117,165902235,331804471,663608942,1327217884,2654435769,5308871538

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

%H Clark Kimberling, <a href="/A293322/b293322.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor((r*2^n)), where r = (-1+sqrt(5))/2.

%F a(n) = A293323(n) - 1.

%t z = 120; r = -1+GoldenRatio;

%t Table[Floor[r*2^n], {n, 0, z}]; (* A293322 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293323 *)

%t Table[Round[r*2^n], {n, 0, z}]; (* A293324 *)

%o (PARI) a(n) = 2^n*(sqrt(5)-1)\2; \\ _Altug Alkan_, Oct 08 2017

%Y Cf. A001622, A293313, A293323, A293324.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Oct 07 2017