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 A134861 #45 Mar 29 2025 12:16:20 %S A134861 2,10,15,23,31,36,44,49,57,65,70,78,86,91,99,104,112,120,125,133,138, %T A134861 146,154,159,167,175,180,188,193,201,209,214,222,230,235,243,248,256, %U A134861 264,269,277,282,290,298,303,311,319,324,332,337,345,353,358,366,371 %N A134861 Wythoff BAA numbers. %C A134861 The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BAA = A+2B-3. %C A134861 Also numbers with suffix string 0010, when written in Zeckendorf representation (with leading zero's for the first term). - _A.H.M. Smeets_, Mar 20 2024 %C A134861 The asymptotic density of this sequence is 1/phi^4 = A094214^4 = 0.145898... . - _Amiram Eldar_, Mar 24 2025 %H A134861 A.H.M. Smeets, <a href="/A134861/b134861.txt">Table of n, a(n) for n = 1..20000</a> %H A134861 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. 4. %H A134861 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 A134861 a(n) = B(A(A(n))), n>=1, with A=A000201, the lower Wythoff sequence and B=A001950, the upper Wythoff sequence. %t A134861 A[n_] := Floor[n * GoldenRatio]; B[n_] := Floor[n * GoldenRatio^2]; a[n_] := B[A[A[n]]]; Array[a, 100] (* _Amiram Eldar_, Mar 24 2025 *) %o A134861 (Python) %o A134861 from sympy import floor %o A134861 from mpmath import phi %o A134861 def A(n): return floor(n*phi) %o A134861 def B(n): return floor(n*phi**2) %o A134861 def a(n): return B(A(A(n))) # _Indranil Ghosh_, Jun 10 2017 %o A134861 (Python) %o A134861 from math import isqrt %o A134861 def A134861(n): return 3*((n+isqrt(5*n**2)>>1)-1)+(n<<1) # _Chai Wah Wu_, Aug 10 2022 %Y A134861 Cf. A000201, A001950, A003622, A003623, A035336, A094214, A101864, A134859, A035337, A134860, A134862, A134863, A035338, A134864, A035513. %Y A134861 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 A134861 nonn %O A134861 1,1 %A A134861 _Clark Kimberling_, Nov 14 2007