A293320 Least integer k such that k/2^n > tau^2, where tau = (1+sqrt(5))/2 = golden ratio.

3, 6, 11, 21, 42, 84, 168, 336, 671, 1341, 2681, 5362, 10724, 21447, 42894, 85788, 171576, 343151, 686302, 1372604, 2745208, 5490416, 10980831, 21961661, 43923322, 87846644, 175693287, 351386574, 702773148, 1405546296, 2811092591, 5622185181, 11244370362

Offset: 0

Author

Clark Kimberling, Oct 07 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001622, A293313, A293319, A293321.

Programs

Magma

[Ceiling((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017

Mathematica

z = 120; r = 1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}];   (* A293319 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293320 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293321 *)

Formula

a(n) = ceiling(r*2^n), where r = (3+sqrt(5))/2.

a(n) = A293319(n) + 1.