A293322 Greatest integer k such that k/2^n < 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.

0, 1, 2, 4, 9, 19, 39, 79, 158, 316, 632, 1265, 2531, 5062, 10125, 20251, 40503, 81006, 162013, 324027, 648055, 1296111, 2592222, 5184444, 10368889, 20737779, 41475558, 82951117, 165902235, 331804471, 663608942, 1327217884, 2654435769, 5308871538

Offset

0,3

Links

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

Formula

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

a(n) = A293323(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) = 2^n*(sqrt(5)-1)\2; \\ Altug Alkan, Oct 08 2017

Crossrefs

Cf. A001622, A293313, A293323, A293324.

Sequence in context: A125050 A056186 A265387 * A267157 A054135 A171858

Adjacent sequences: A293319 A293320 A293321 * A293323 A293324 A293325

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2017

Status

approved