A293321 The integer k that minimizes |k/2^n - tau^2|, where tau = (1+sqrt(5))/2 = golden ratio.

3, 5, 10, 21, 42, 84, 168, 335, 670, 1340, 2681, 5362, 10723, 21447, 42894, 85788, 171575, 343151, 686302, 1372604, 2745208, 5490415, 10980830, 21961661, 43923322, 87846643, 175693287, 351386574, 702773148, 1405546295, 2811092590, 5622185181, 11244370361

Offset

0,1

Links

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

Formula

a(n) = floor(1/2 + r*2^n), where r = (3+sqrt(5))/2.

a(n) = A293319(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293316(n).

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

(PARI) a(n) = (2^n*(3+sqrt(5))+1)\2; \\ Altug Alkan, Oct 08 2017

Crossrefs

Cf. A001622, A293313, A293319, A293320.

Sequence in context: A037183 A214209 A024424 * A284237 A241436 A018107

Adjacent sequences: A293318 A293319 A293320 * A293322 A293323 A293324

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2017

Status

approved