A004955 -id:A004955 - cp's OEIS frontend

A004937 a(n) = round(n*phi^2), where phi is the golden ratio, A001622.

0, 3, 5, 8, 10, 13, 16, 18, 21, 24, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65, 68, 71, 73, 76, 79, 81, 84, 86, 89, 92, 94, 97, 99, 102, 105, 107, 110, 113, 115, 118, 120, 123, 126, 128, 131, 134, 136, 139, 141, 144, 147, 149, 152, 154, 157

Offset: 0

N. J. A. Sloane

nonn

Amiram Eldar, Table of n, a(n) for n = 0..10000
Benoit Cloitre and Jeffrey Shallit, Some Fibonacci-Related Sequences, arXiv:2312.11706 [math.CO], 2023.

Cf. A001622, A104457.

Cf. A004938 - A004955, A007067.

[Round((3+Sqrt(5))*n/2): n in [0..80]]; // G. C. Greubel, Sep 13 2023

a[n_] := Round[n*GoldenRatio^2]; Array[a, 50, 0] (* Amiram Eldar, Jun 17 2022 *)

a(n)=round(n*(sqrt(5)+3)/2) \\ Charles R Greathouse IV, Aug 28 2016

[round(golden_ratio^2*n) for n in range(81)] # G. C. Greubel, Sep 13 2023

A004938 a(n) = round(n*phi^3), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 4, 8, 13, 17, 21, 25, 30, 34, 38, 42, 47, 51, 55, 59, 64, 68, 72, 76, 80, 85, 89, 93, 97, 102, 106, 110, 114, 119, 123, 127, 131, 136, 140, 144, 148, 152, 157, 161, 165, 169, 174, 178, 182, 186, 191, 195, 199

Offset: 0

N. J. A. Sloane

nonn

Nearest integer to n*phi^3.

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A004937, A004939 - A004955.

Cf. A001622.

[Round((2+Sqrt(5))*n): n in [0..80]]; // G. C. Greubel, Oct 17 2023

Round[GoldenRatio^3*Range[0, 80]] (* G. C. Greubel, Oct 17 2023 *)

a(n) = round(n*(((sqrt(5)+1))/2)^3); \\ Michel Marcus, Aug 28 2016

[round(golden_ratio^3*n) for n in range(81)] # G. C. Greubel, Oct 17 2023

A004975 a(n) = ceiling(n*phi^20), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 15127, 30254, 45381, 60508, 75635, 90762, 105889, 121016, 136143, 151270, 166397, 181524, 196651, 211778, 226905, 242032, 257159, 272286, 287413, 302540, 317667, 332794, 347921, 363048, 378175, 393302, 408429, 423556, 438683, 453810, 468937, 484064, 499191, 514318, 529445, 544572, 559699

Offset: 0

N. J. A. Sloane

nonn

Not the same as A004955: a(n) != A004955(n) for n=7564. [Joerg Arndt, Sep 17 2013]

Tanya Khovanova, Non Recursions

With[{c=GoldenRatio^20},Ceiling[c*Range[0,40]]] (* Harvey P. Dale, Jul 17 2018 *)

a(n) >= A004955(n). [R. J. Mathar, Oct 28 2008]

cp's OEIS Frontend

A004937 a(n) = round(n*phi^2), where phi is the golden ratio, A001622.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

SageMath

A004938 a(n) = round(n*phi^3), where phi is the golden ratio, A001622.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

SageMath

A004975 a(n) = ceiling(n*phi^20), where phi is the golden ratio, A001622.

Views

Author

Keywords

Comments

Links

Programs

Mathematica

Formula