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)
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.
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 14 2007
STATUS
approved