A134862 Wythoff ABB numbers.

8, 21, 29, 42, 55, 63, 76, 84, 97, 110, 118, 131, 144, 152, 165, 173, 186, 199, 207, 220, 228, 241, 254, 262, 275, 288, 296, 309, 317, 330, 343, 351, 364, 377, 385, 398, 406, 419, 432, 440, 453, 461, 474, 487, 495, 508, 521, 529, 542, 550, 563, 576, 584, 597

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..54.

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

Formula

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

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 A(B(B(n))) # Indranil Ghosh, Jun 10 2017
(Python)
from math import isqrt
def A134862(n): return 5*(n+isqrt(5*n**2)>>1)+3*n # Chai Wah Wu, Aug 10 2022

Crossrefs

Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, A134863, 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: A321439 A271921 A003249 * A302253 A090206 A139590

Adjacent sequences: A134859 A134860 A134861 * A134863 A134864 A134865

Keyword

nonn

Author

Clark Kimberling, Nov 14 2007

Status

approved