A293321 -id:A293321 - cp's OEIS frontend

A293319 Greatest integer k such that k/2^n < tau^2, where tau = (1+sqrt(5))/2 = golden ratio.

2, 5, 10, 20, 41, 83, 167, 335, 670, 1340, 2680, 5361, 10723, 21446, 42893, 85787, 171575, 343150, 686301, 1372603, 2745207, 5490415, 10980830, 21961660, 43923321, 87846643, 175693286, 351386573, 702773147, 1405546295, 2811092590, 5622185180, 11244370361

Offset: 0

Clark Kimberling, Oct 07 2017

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

Cf. A001622, A293313, A293320, A293321.

[Floor((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017

z = 120; r = 1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}];   (* A293319 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293320 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293321 *)

a(n) = floor((r*2^n)), where r = (3+sqrt(5))/2.

a(n) = A293320(n) - 1.

A293320 Least integer k such that k/2^n > tau^2, where tau = (1+sqrt(5))/2 = golden ratio.

Original entry on oeis.org

3, 6, 11, 21, 42, 84, 168, 336, 671, 1341, 2681, 5362, 10724, 21447, 42894, 85788, 171576, 343151, 686302, 1372604, 2745208, 5490416, 10980831, 21961661, 43923322, 87846644, 175693287, 351386574, 702773148, 1405546296, 2811092591, 5622185181, 11244370362

Offset: 0

Clark Kimberling, Oct 07 2017

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

Cf. A001622, A293313, A293319, A293321.

[Ceiling((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017

z = 120; r = 1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}];   (* A293319 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293320 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293321 *)

a(n) = ceiling(r*2^n), where r = (3+sqrt(5))/2.

a(n) = A293319(n) + 1.

cp's OEIS Frontend

A293319 Greatest integer k such that k/2^n < tau^2, where tau = (1+sqrt(5))/2 = golden ratio.

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