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

0,3

Links

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

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).

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 *)

Crossrefs

Cf. A001622, A293322, A293323.

Sequence in context: A222082 A327287 A296122 * A284904 A084215 A024810

Adjacent sequences: A293321 A293322 A293323 * A293325 A293326 A293327

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2017

Status

approved