A293329 The integer k that minimizes |k/2^n - sqrt(1/3)|.

1, 1, 2, 5, 9, 18, 37, 74, 148, 296, 591, 1182, 2365, 4730, 9459, 18919, 37837, 75674, 151349, 302698, 605396, 1210791, 2421583, 4843165, 9686330, 19372660, 38745321, 77490641, 154981283, 309962566, 619925131, 1239850262, 2479700525, 4959401049, 9918802098

Offset: 0

Author

Clark Kimberling, Oct 10 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A002194, A094386, A293327, A293328.

Programs

Mathematica

z = 120; r = Sqrt[1/3];
Table[Floor[r*2^n], {n, 0, z}];   (* A293327 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293328 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293329 *)

Formula

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

a(n) = A293327(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293328(n).