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A293314 Least integer k such that k/2^n > (1+sqrt(5))/2 (the golden ratio).

%I A293314 #9 Oct 06 2017 21:35:02
%S A293314 2,4,7,13,26,52,104,208,415,829,1657,3314,6628,13255,26510,53020,
%T A293314 106040,212079,424158,848316,1696632,3393264,6786527,13573053,
%U A293314 27146106,54292212,108584423,217168846,434337692,868675384,1737350767,3474701533,6949403066
%N A293314 Least integer k such that k/2^n > (1+sqrt(5))/2 (the golden ratio).
%H A293314 Clark Kimberling, <a href="/A293314/b293314.txt">Table of n, a(n) for n = 0..1000</a>
%F A293314 a(n) = ceiling(r*2^n), where r = (1+sqrt(5))/2.
%F A293314 a(n) = A293313(n) + 1.
%p A293314 A293314:=n->ceil(2^n*(1+sqrt(5))/2): seq(A293314(n), n=0..40); # _Wesley Ivan Hurt_, Oct 06 2017
%t A293314 z = 120; r = GoldenRatio;
%t A293314 Table[Floor[r*2^n], {n, 0, z}];   (* A293313 *)
%t A293314 Table[Ceiling[r*2^n], {n, 0, z}]; (* A293314 *)
%t A293314 Table[Round[r*2^n], {n, 0, z}];   (* A293315 *)
%o A293314 (PARI) a(n) = ceil(2^n*(1+sqrt(5))/2) \\ _Altug Alkan_, Oct 06 2017
%Y A293314 Cf. A001622, A293313, A293315.
%K A293314 nonn,easy
%O A293314 0,1
%A A293314 _Clark Kimberling_, Oct 06 2017