A293326 - OEIS

%I #10 Dec 11 2023 10:45:28

%S 2,3,7,14,28,55,111,222,443,887,1774,3547,7094,14189,28378,56756,

%T 113512,227023,454047,908093,1816187,3632374,7264748,14529495,

%U 29058991,58117981,116235962,232471924,464943848,929887697,1859775393,3719550787,7439101574

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

%H Clark Kimberling, <a href="/A293326/b293326.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%t z = 120; r = Sqrt[3];

%t Table[Floor[r*2^n], {n, 0, z}];   (* A094386 *)

%t Table[Ceiling[r*2^n], {n, 0, z}]; (* A293325 *)

%t Table[Round[r*2^n], {n, 0, z}]; (* A293326 *)

%o (Python)

%o from math import isqrt

%o 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

%Y Cf. A002194, A094386, A293325.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Oct 09 2017