cp's OEIS Frontend

A293323 Least integer k such that k/2^n > 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.

%I A293323 #6 Oct 09 2017 08:25:17
%S A293323 1,2,3,5,10,20,40,80,159,317,633,1266,2532,5063,10126,20252,40504,
%T A293323 81007,162014,324028,648056,1296112,2592223,5184445,10368890,20737780,
%U A293323 41475559,82951118,165902236,331804472,663608943,1327217885,2654435770,5308871539
%N A293323 Least integer k such that k/2^n > 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.
%H A293323 Clark Kimberling, <a href="/A293323/b293323.txt">Table of n, a(n) for n = 0..1000</a>
%F A293323 a(n) = ceiling(r*2^n), where r = (-1+sqrt(5))/2.
%F A293323 a(n) = A293322(n) + 1.
%t A293323 z = 120; r = -1+GoldenRatio;
%t A293323 Table[Floor[r*2^n], {n, 0, z}];   (* A293322 *)
%t A293323 Table[Ceiling[r*2^n], {n, 0, z}]; (* A293323 *)
%t A293323 Table[Round[r*2^n], {n, 0, z}];   (* A293324 *)
%o A293323 (PARI) a(n) = ceil(2^(n-1)*(sqrt(5)-1)); \\ _Altug Alkan_, Oct 08 2017
%Y A293323 Cf. A001622, A293313, A293322, A293324.
%K A293323 nonn,easy
%O A293323 0,2
%A A293323 _Clark Kimberling_, Oct 07 2017