A293314 Least integer k such that k/2^n > (1+sqrt(5))/2 (the golden ratio).

2, 4, 7, 13, 26, 52, 104, 208, 415, 829, 1657, 3314, 6628, 13255, 26510, 53020, 106040, 212079, 424158, 848316, 1696632, 3393264, 6786527, 13573053, 27146106, 54292212, 108584423, 217168846, 434337692, 868675384, 1737350767, 3474701533, 6949403066

Offset

0,1

Links

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

Formula

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

a(n) = A293313(n) + 1.

Maple

A293314:=n->ceil(2^n*(1+sqrt(5))/2): seq(A293314(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) = ceil(2^n*(1+sqrt(5))/2) \\ Altug Alkan, Oct 06 2017

Crossrefs

Cf. A001622, A293313, A293315.

Sequence in context: A342764 A262267 A068031 * A023431 A025246 A256942

Adjacent sequences: A293311 A293312 A293313 * A293315 A293316 A293317

Keyword

nonn,easy

Author

Clark Kimberling, Oct 06 2017

Status

approved