A293323 Least integer k such that k/2^n > 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.

1, 2, 3, 5, 10, 20, 40, 80, 159, 317, 633, 1266, 2532, 5063, 10126, 20252, 40504, 81007, 162014, 324028, 648056, 1296112, 2592223, 5184445, 10368890, 20737780, 41475559, 82951118, 165902236, 331804472, 663608943, 1327217885, 2654435770, 5308871539

Offset

0,2

Links

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

Formula

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

a(n) = A293322(n) + 1.

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 *)

Prog

(PARI) a(n) = ceil(2^(n-1)*(sqrt(5)-1)); \\ Altug Alkan, Oct 08 2017

Crossrefs

Cf. A001622, A293313, A293322, A293324.

Sequence in context: A251703 A057755 A262482 * A257113 A367216 A352945

Adjacent sequences: A293320 A293321 A293322 * A293324 A293325 A293326

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2017

Status

approved