A293315 - OEIS

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A293315

The integer k that minimizes |k/2^n - r|, where r = golden ratio.

2, 3, 6, 13, 26, 52, 104, 207, 414, 828, 1657, 3314, 6627, 13255, 26510, 53020, 106039, 212079, 424158, 848316, 1696632, 3393263, 6786526, 13573053, 27146106, 54292211, 108584423, 217168846, 434337692, 868675383, 1737350766, 3474701533, 6949403065

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

OFFSET

0,1

LINKS

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

FORMULA

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

a(n) = A293313(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293313(n).

MAPLE

A293315:=n->floor(1/2+2^n*(1+sqrt(5))/2): seq(A293315(n), n=0..40); # Wesley Ivan Hurt, Oct 06 2017

MATHEMATICA

z = 120; r = GoldenRatio;