A293324 The integer k that minimizes |k/2^n - 1/tau|, where tau = (1+sqrt(5))/2 = golden ratio.

1, 1, 2, 5, 10, 20, 40, 79, 158, 316, 633, 1266, 2531, 5063, 10126, 20252, 40503, 81007, 162014, 324028, 648056, 1296111, 2592222, 5184445, 10368890, 20737779, 41475559, 82951118, 165902236, 331804471, 663608942, 1327217885, 2654435769, 5308871539

Offset: 0

Author

Clark Kimberling, Oct 07 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001622, A293322, A293323.

Programs

Mathematica

z = 120; r = -1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}];   (* A293322 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293323 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293324 *)

Formula

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

a(n) = A293322(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293323(n).