A293313 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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;