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A134863 Wythoff BAB numbers. 9
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 (list; graph; refs; listen; history; text; internal format)
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
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
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
KEYWORD
nonn,changed
AUTHOR
Clark Kimberling, Nov 14 2007
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)