This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A134863 #42 Mar 29 2025 12:15:48
%S A134863 7,20,28,41,54,62,75,83,96,109,117,130,143,151,164,172,185,198,206,
%T A134863 219,227,240,253,261,274,287,295,308,316,329,342,350,363,376,384,397,
%U A134863 405,418,431,439,452,460,473,486,494,507,520,528,541,549,562,575,583,596
%N A134863 Wythoff BAB numbers.
%C A134863 The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BAB = 2A+3B-1.
%C A134863 Also numbers with suffix string 1010, when written in Zeckendorf representation. - _A.H.M. Smeets_, Mar 24 2024
%C A134863 The asymptotic density of this sequence is 1/phi^5 = phi^5 - 11 = A244593 - 4 = 0.0901699... . - _Amiram Eldar_, Mar 24 2025
%H A134863 A.H.M. Smeets, <a href="/A134863/b134863.txt">Table of n, a(n) for n = 1..20000</a>
%H A134863 Jon Asier Bárcena-Petisco, Luis Martínez, María Merino, Juan Manuel Montoya, and Antonio Vera-López, <a href="https://arxiv.org/abs/2503.19696">Fibonacci-like partitions and their associated piecewise-defined permutations</a>, arXiv:2503.19696 [math.CO], 2025. See p. 5.
%H A134863 Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Kimberling/kimberling719a.html">Complementary equations and Wythoff Sequences</a>, Journal of Integer Sequences 11 (2008), Article 08.3.3.
%F A134863 a(n) = B(A(B(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence.
%F A134863 From _A.H.M. Smeets_, Mar 24 2024: (Start)
%F A134863 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.
%F A134863 Equals {A035336}\{A134861} (= Wythoff BA \ Wythoff BAA). (End)
%t A134863 A[n_] := Floor[n * GoldenRatio]; B[n_] := Floor[n * GoldenRatio^2]; a[n_] := B[A[B[n]]]; Array[a, 100] (* _Amiram Eldar_, Mar 24 2025 *)
%o A134863 (Python)
%o A134863 from sympy import floor
%o A134863 from mpmath import phi
%o A134863 def A(n): return floor(n*phi)
%o A134863 def B(n): return floor(n*phi**2)
%o A134863 def a(n): return B(A(B(n))) # _Indranil Ghosh_, Jun 10 2017
%o A134863 (Python)
%o A134863 from math import isqrt
%o A134863 def A134863(n): return 5*(n+isqrt(5*n**2)>>1)+3*n-1 # _Chai Wah Wu_, Aug 11 2022
%Y A134863 Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, A134862, A035338, A134864, A035513, A244593.
%Y A134863 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.
%K A134863 nonn
%O A134863 1,1
%A A134863 _Clark Kimberling_, Nov 14 2007