A035338 4th column of Wythoff array.

5, 18, 26, 39, 52, 60, 73, 81, 94, 107, 115, 128, 141, 149, 162, 170, 183, 196, 204, 217, 225, 238, 251, 259, 272, 285, 293, 306, 314, 327, 340, 348, 361, 374, 382, 395, 403, 416, 429, 437, 450, 458, 471, 484, 492, 505, 518, 526, 539, 547, 560, 573, 581, 594

Offset

0,1

Comments

The asymptotic density of this sequence is 1/phi^5 = phi^5 - 11 = A244593 - 4 = 0.0901699... . - Amiram Eldar, Mar 24 2025

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Jon Asier Bárcena-Petisco, Luis Martínez, María Merino, Juan Manuel Montoya, and Antonio Vera-López, Fibonacci-like partitions and their associated piecewise-defined permutations, arXiv:2503.19696 [math.CO], 2025. See p. 5.

John H. Conway and N. J. A. Sloane, Notes on the Para-Fibonacci and related sequences.

Clark Kimberling, Complementary equations and Wythoff Sequences, JIS, Vol. 11 (2008), Article 08.3.3.

N. J. A. Sloane, Classic Sequences.

Maple

t := (1+sqrt(5))/2 ; [ seq(5*floor((n+1)*t)+3*n, n=0..80) ];

Mathematica

f[n_] := 5 Floor[(n + 1) GoldenRatio] + 3n; Array[f, 54, 0] (* Robert G. Wilson v, Dec 11 2017 *)

Prog

(Python)
from math import isqrt
def A035338(n): return 5*(n+1+isqrt(5*(n+1)**2)>>1)+3*n # Chai Wah Wu, Aug 11 2022

Crossrefs

Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864. The eight triples AAA, AAB, ..., BBB are A134859, A134860, A035337, A134862, A134861, A134863, A035338, A134864, resp.

Cf. A035513, A244593.

Sequence in context: A022142 A078648 A364607 * A055371 A034098 A034108

Adjacent sequences: A035335 A035336 A035337 * A035339 A035340 A035341

Keyword

nonn

Author

N. J. A. Sloane and J. H. Conway

Status

approved