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

0,1

Links

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

Formula

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

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

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 *)

Prog

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

Crossrefs

Cf. A001622, A293313, A293319, A293321.

Sequence in context: A261392 A251655 A132658 * A024495 A360045 A354695

Adjacent sequences: A293317 A293318 A293319 * A293321 A293322 A293323

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2017

Status

approved