A293314 - OEIS

%I #9 Oct 06 2017 21:35:02

%S 2,4,7,13,26,52,104,208,415,829,1657,3314,6628,13255,26510,53020,

%T 106040,212079,424158,848316,1696632,3393264,6786527,13573053,

%U 27146106,54292212,108584423,217168846,434337692,868675384,1737350767,3474701533,6949403066

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

%H Clark Kimberling, <a href="/A293314/b293314.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = A293313(n) + 1.

%p A293314:=n->ceil(2^n*(1+sqrt(5))/2): seq(A293314(n), n=0..40); # _Wesley Ivan Hurt_, Oct 06 2017

%t z = 120; r = GoldenRatio;

%t Table[Floor[r*2^n], {n, 0, z}];   (* A293313 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293314 *)

%t Table[Round[r*2^n], {n, 0, z}];   (* A293315 *)

%o (PARI) a(n) = ceil(2^n*(1+sqrt(5))/2) \\ _Altug Alkan_, Oct 06 2017

%Y Cf. A001622, A293313, A293315.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Oct 06 2017