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A293315 The integer k that minimizes |k/2^n - r|, where r = golden ratio. 3
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;

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

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Last modified October 21 09:09 EDT 2020. Contains 337911 sequences. (Running on oeis4.)