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%I #9 Sep 08 2022 08:46:19
%S 3,6,11,21,42,84,168,336,671,1341,2681,5362,10724,21447,42894,85788,
%T 171576,343151,686302,1372604,2745208,5490416,10980831,21961661,
%U 43923322,87846644,175693287,351386574,702773148,1405546296,2811092591,5622185181,11244370362
%N Least integer k such that k/2^n > tau^2, where tau = (1+sqrt(5))/2 = golden ratio.
%H Clark Kimberling, <a href="/A293320/b293320.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = ceiling(r*2^n), where r = (3+sqrt(5))/2.
%F a(n) = A293319(n) + 1.
%t z = 120; r = 1+GoldenRatio;
%t Table[Floor[r*2^n], {n, 0, z}]; (* A293319 *)
%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293320 *)
%t Table[Round[r*2^n], {n, 0, z}]; (* A293321 *)
%o (Magma) [Ceiling((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // _Vincenzo Librandi_, Oct 08 2017
%Y Cf. A001622, A293313, A293319, A293321.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Oct 07 2017