cp's OEIS Frontend

A293320 Least integer k such that k/2^n > tau^2, where tau = (1+sqrt(5))/2 = golden ratio.

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