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

Offset: 0

Author

Clark Kimberling, Oct 06 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001622, A293313, A293314.

Programs

Magma

[Floor((2^n*(1+Sqrt(5))+1)/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017

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;
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 *)

PARI

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

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).