A293319 Greatest integer k such that k/2^n < tau^2, where tau = (1+sqrt(5))/2 = golden ratio.

2, 5, 10, 20, 41, 83, 167, 335, 670, 1340, 2680, 5361, 10723, 21446, 42893, 85787, 171575, 343150, 686301, 1372603, 2745207, 5490415, 10980830, 21961660, 43923321, 87846643, 175693286, 351386573, 702773147, 1405546295, 2811092590, 5622185180, 11244370361

Offset

0,1

Links

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

Formula

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

a(n) = A293320(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) [Floor((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017

Crossrefs

Cf. A001622, A293313, A293320, A293321.

Sequence in context: A002460 A266613 A266462 * A267589 A006836 A129847

Adjacent sequences: A293316 A293317 A293318 * A293320 A293321 A293322

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2017

Status

approved