A293324 -id:A293324 - cp's OEIS frontend

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

Clark Kimberling, Oct 07 2017

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

Cf. A001622, A293313, A293323, 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) = 2^n*(sqrt(5)-1)\2; \\ Altug Alkan, Oct 08 2017

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

a(n) = A293323(n) - 1.

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

Original entry on oeis.org

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.

cp's OEIS Frontend

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

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