A293322 -id:A293322 - cp's OEIS frontend

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

Clark Kimberling, Oct 07 2017

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

Cf. A001622, A293313, A293322, A293324.

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 *)

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

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

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

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

Original entry on oeis.org

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

Clark Kimberling, Oct 07 2017

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

Cf. A001622, A293322, A293323.

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 *)

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).

cp's OEIS Frontend

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

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