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A101864 Wythoff BB numbers. 21

%I #34 Dec 17 2021 01:08:00

%S 5,13,18,26,34,39,47,52,60,68,73,81,89,94,102,107,115,123,128,136,141,

%T 149,157,162,170,178,183,191,196,204,212,217,225,233,238,246,251,259,

%U 267,272,280,285,293,301,306,314,322,327,335,340,348,356,361,369,374,382,390,395

%N Wythoff BB numbers.

%C a(n)-3 are also the positions of 1 in A188436. - _Federico Provvedi_, Nov 22 2018

%H Muniru A Asiru, <a href="/A101864/b101864.txt">Table of n, a(n) for n = 1..2000</a>

%H J.-P. Allouche and F. M. Dekking, <a href="https://arxiv.org/abs/1809.03424">Generalized Beatty sequences and complementary triples</a>, arXiv:1809.03424 [math.NT], 2018.

%H C. Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Kimberling/kimberling719a.html">Complementary equations and Wythoff Sequences</a>, JIS 11 (2008) 08.3.3.

%H Clark Kimberling, <a href="https://doi.org/10.4171/EM/468">Intriguing infinite words composed of zeros and ones</a>, Elemente der Mathematik (2021).

%H C. Kimberling and K. 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, 123 (No. 2, 2016), 267-273.

%F a(n) = B(B(n)), n>=1, with B(k)=A001950(k) (Wythoff B-numbers). a(0)=0 with B(0)=0.

%p b:=n->floor(n*((1+sqrt(5))/2)^2): seq(b(b(n)),n=1..60); # _Muniru A Asiru_, Dec 05 2018

%t b[n_] := Floor[n * GoldenRatio^2]; a[n_] := b[b[n]]; Array[a, 60] (* _Amiram Eldar_, Nov 22 2018 *)

%o (Python)

%o from sympy import S

%o for n in range(1,60): print(int(S.GoldenRatio**2*(int(n*S.GoldenRatio**2))), end=', ') # _Stefano Spezia_, Dec 06 2018

%Y Second row of A101858.

%Y Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jan 28 2005

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Last modified April 25 08:20 EDT 2024. Contains 371964 sequences. (Running on oeis4.)