A134863 Wythoff BAB numbers.

7, 20, 28, 41, 54, 62, 75, 83, 96, 109, 117, 130, 143, 151, 164, 172, 185, 198, 206, 219, 227, 240, 253, 261, 274, 287, 295, 308, 316, 329, 342, 350, 363, 376, 384, 397, 405, 418, 431, 439, 452, 460, 473, 486, 494, 507, 520, 528, 541, 549, 562, 575, 583, 596

Offset

1,1

Comments

The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BAB=2A+3B-1.

Also numbers with suffix string 1010, when written in Zeckendorf representation. - A.H.M. Smeets, Mar 24 2024

Links

A.H.M. Smeets, Table of n, a(n) for n = 1..20000

Clark Kimberling, Complementary equations and Wythoff Sequences, Journal of Integer Sequences 11 (2008) Article 08.3.3.

Formula

a(n) = B(A(B(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence.

From A.H.M. Smeets, Mar 24 2024: (Start)

a(n) = 2*A(n) + 3*B(n) - 1 (see Clark Kimberling 2008), with A=A000201, B=A001950, the lower and upper Wythoff sequences, respectively.

Equals {A035336}\{A134861} (= Wythoff BA \ Wythoff BAA). (End)

Prog

(Python)
from sympy import floor
from mpmath import phi
def A(n): return floor(n*phi)
def B(n): return floor(n*phi**2)
def a(n): return B(A(B(n))) # Indranil Ghosh, Jun 10 2017
(Python)
from math import isqrt
def A134863(n): return 5*(n+isqrt(5*n**2)>>1)+3*n-1 # Chai Wah Wu, Aug 11 2022

Crossrefs

Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, A134862, A035338, A134864, A035513.

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.

Sequence in context: A070413 A015243 A055069 * A214924 A333858 A319966

Adjacent sequences: A134860 A134861 A134862 * A134864 A134865 A134866

Keyword

nonn

Author

Clark Kimberling, Nov 14 2007

Status

approved