A293313 Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio).

1, 3, 6, 12, 25, 51, 103, 207, 414, 828, 1656, 3313, 6627, 13254, 26509, 53019, 106039, 212078, 424157, 848315, 1696631, 3393263, 6786526, 13573052, 27146105, 54292211, 108584422, 217168845, 434337691, 868675383, 1737350766, 3474701532, 6949403065

Offset

0,2

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

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

a(n) = A293314(n) - 1.

Maple

A293313:=n->floor(2^n*(1+sqrt(5))/2): seq(A293313(n), n=0..40); # Wesley Ivan Hurt, Oct 06 2017

Mathematica

z = 120; r = GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}];   (* A293313 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293314 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293315 *)

Prog

(PARI) a(n) = (2^n*(1+sqrt(5)))\2; \\ Altug Alkan, Oct 06 2017

Crossrefs

Cf. A001622, A293314, A293315.

Sequence in context: A136444 A077854 A265700 * A267539 A243722 A187260

Adjacent sequences: A293310 A293311 A293312 * A293314 A293315 A293316

Keyword

nonn,easy

Author

Clark Kimberling, Oct 06 2017

Status

approved