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

Author

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

Keywords

• nonn

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.

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.

Programs

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 *)

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