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

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, A293315.

Programs

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 *)

PARI

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

Formula

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

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