A101864 Wythoff BB numbers.

5, 13, 18, 26, 34, 39, 47, 52, 60, 68, 73, 81, 89, 94, 102, 107, 115, 123, 128, 136, 141, 149, 157, 162, 170, 178, 183, 191, 196, 204, 212, 217, 225, 233, 238, 246, 251, 259, 267, 272, 280, 285, 293, 301, 306, 314, 322, 327, 335, 340, 348, 356, 361, 369, 374, 382, 390, 395

Offset

1,1

Comments

a(n)-3 are also the positions of 1 in A188436. - Federico Provvedi, Nov 22 2018

Links

Muniru A Asiru, Table of n, a(n) for n = 1..2000

J.-P. Allouche and F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424 [math.NT], 2018.

C. Kimberling, Complementary equations and Wythoff Sequences, JIS 11 (2008) 08.3.3.

Clark Kimberling, Intriguing infinite words composed of zeros and ones, Elemente der Mathematik (2021).

C. Kimberling and K. B. Stolarsky, Slow Beatty sequences, devious convergence, and partitional divergence, Amer. Math. Monthly, 123 (No. 2, 2016), 267-273.

Formula

a(n) = B(B(n)), n>=1, with B(k)=A001950(k) (Wythoff B-numbers). a(0)=0 with B(0)=0.

Maple

b:=n->floor(n*((1+sqrt(5))/2)^2): seq(b(b(n)), n=1..60); # Muniru A Asiru, Dec 05 2018

Mathematica

b[n_] := Floor[n * GoldenRatio^2]; a[n_] := b[b[n]]; Array[a, 60] (* Amiram Eldar, Nov 22 2018 *)

Prog

(Python)
from sympy import S
for n in range(1, 60): print(int(S.GoldenRatio**2*(int(n*S.GoldenRatio**2))), end=', ') # Stefano Spezia, Dec 06 2018

Crossrefs

Second row of A101858.

Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864.

Sequence in context: A120062 A081769 A188030 * A190432 A197563 A022138

Adjacent sequences: A101861 A101862 A101863 * A101865 A101866 A101867

Keyword

nonn

Author

N. J. A. Sloane, Jan 28 2005

Status

approved