A293333 The integer k that minimizes |k/2^n - sqrt(5)|.

2, 4, 9, 18, 36, 72, 143, 286, 572, 1145, 2290, 4579, 9159, 18318, 36636, 73271, 146543, 293086, 586172, 1172344, 2344687, 4689374, 9378749, 18757498, 37514995, 75029991, 150059982, 300119964, 600239927, 1200479854, 2400959709, 4801919417, 9603838835

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(5).

a(n) = A293331(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293332(n).

Mathematica

z = 120; r = Sqrt[5];
Table[Floor[r*2^n], {n, 0, z}];   (* A293331 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293332 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293333 *)

Prog

(Python)
from math import isqrt
def A293333(n): return (k:=isqrt(m:=5*(1<<(n<<1))))+int((m-k*(k+1)<<2)-1>=0) # Chai Wah Wu, Jul 28 2022

Crossrefs

Cf. A001633, A293331, A293332.

Sequence in context: A138196 A298404 A101351 * A111662 A253585 A119027

Adjacent sequences: A293330 A293331 A293332 * A293334 A293335 A293336

Keyword

nonn,easy

Author

Clark Kimberling, Oct 10 2017

Status

approved