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 A101864 #43 Mar 29 2025 12:16:35 %S A101864 5,13,18,26,34,39,47,52,60,68,73,81,89,94,102,107,115,123,128,136,141, %T A101864 149,157,162,170,178,183,191,196,204,212,217,225,233,238,246,251,259, %U A101864 267,272,280,285,293,301,306,314,322,327,335,340,348,356,361,369,374,382,390,395 %N A101864 Wythoff BB numbers. %C A101864 a(n)-3 are also the positions of 1 in A188436. - _Federico Provvedi_, Nov 22 2018 %C A101864 The asymptotic density of this sequence is 1/phi^4 = A094214^4 = 0.145898... . - _Amiram Eldar_, Mar 24 2025 %H A101864 Muniru A Asiru, <a href="/A101864/b101864.txt">Table of n, a(n) for n = 1..2000</a> %H A101864 Jean-Paul Allouche and F. Michel Dekking, <a href="https://arxiv.org/abs/1809.03424">Generalized Beatty sequences and complementary triples</a>, arXiv:1809.03424 [math.NT], 2018-2019. %H A101864 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 A101864 Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Kimberling/kimberling719a.html">Complementary equations and Wythoff Sequences</a>, JIS 11 (2008), Article 08.3.3. %H A101864 Clark Kimberling, <a href="https://doi.org/10.4171/EM/468">Intriguing infinite words composed of zeros and ones</a>, Elemente der Mathematik, Vol. 78, No. 2 (2021), pp. 1-8. %H A101864 Clark Kimberling and Kenneth B. Stolarsky, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.3.267">Slow Beatty sequences, devious convergence, and partitional divergence</a>, Amer. Math. Monthly, Vol. 123, No. 2 (2016), 267-273. %F A101864 a(n) = B(B(n)), n>=1, with B(k)=A001950(k) (Wythoff B-numbers). a(0)=0 with B(0)=0. %p A101864 b:=n->floor(n*((1+sqrt(5))/2)^2): seq(b(b(n)),n=1..60); # _Muniru A Asiru_, Dec 05 2018 %t A101864 b[n_] := Floor[n * GoldenRatio^2]; a[n_] := b[b[n]]; Array[a, 60] (* _Amiram Eldar_, Nov 22 2018 *) %o A101864 (Python) %o A101864 from sympy import S %o A101864 for n in range(1,60): print(int(S.GoldenRatio**2*(int(n*S.GoldenRatio**2))), end=', ') # _Stefano Spezia_, Dec 06 2018 %Y A101864 Second row of A101858. %Y A101864 Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864. %Y A101864 Cf. A094214, A188436. %K A101864 nonn %O A101864 1,1 %A A101864 _N. J. A. Sloane_, Jan 28 2005