A293326 The integer k that minimizes |k/2^n - sqrt(3)|.

2, 3, 7, 14, 28, 55, 111, 222, 443, 887, 1774, 3547, 7094, 14189, 28378, 56756, 113512, 227023, 454047, 908093, 1816187, 3632374, 7264748, 14529495, 29058991, 58117981, 116235962, 232471924, 464943848, 929887697, 1859775393, 3719550787, 7439101574

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 = sqrt(3).

a(n) = A094386(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293325(n).

Mathematica

z = 120; r = Sqrt[3];
Table[Floor[r*2^n], {n, 0, z}];   (* A094386 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293325 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293326 *)

Prog

(Python)
from math import isqrt
def A293326(n): return (k:=isqrt(m:=3*(1<<(n<<1))))+int((m-k*(k+1)<<2)-1>=0) # Chai Wah Wu, Jul 28 2022

Crossrefs

Cf. A002194, A094386, A293325.

Sequence in context: A333342 A078043 A294627 * A308092 A262765 A340163

Adjacent sequences: A293323 A293324 A293325 * A293327 A293328 A293329

Keyword

nonn,easy

Author

Clark Kimberling, Oct 09 2017

Status

approved