|
%I #10 Oct 06 2017 21:34:55
%S 1,3,6,12,25,51,103,207,414,828,1656,3313,6627,13254,26509,53019,
%T 106039,212078,424157,848315,1696631,3393263,6786526,13573052,
%U 27146105,54292211,108584422,217168845,434337691,868675383,1737350766,3474701532,6949403065
%N Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio).
%H Clark Kimberling, <a href="/A293313/b293313.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = floor(r*2^n), where r = (1+sqrt(5))/2.
%F a(n) = A293314(n) - 1.
%p A293313:=n->floor(2^n*(1+sqrt(5))/2): seq(A293313(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) = (2^n*(1+sqrt(5)))\2; \\ _Altug Alkan_, Oct 06 2017
%Y Cf. A001622, A293314, A293315.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Oct 06 2017
|
