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

0,1

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;
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))+1)\2; \\ Altug Alkan, Oct 06 2017
(Magma) [Floor((2^n*(1+Sqrt(5))+1)/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017

Crossrefs

Cf. A001622, A293313, A293314.

Sequence in context: A079662 A290991 A007910 * A052702 A058766 A127601

Adjacent sequences: A293312 A293313 A293314 * A293316 A293317 A293318

Keyword

nonn,easy

Author

Clark Kimberling, Oct 06 2017

Status

approved