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A101864
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Wythoff BB numbers.
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21
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5, 13, 18, 26, 34, 39, 47, 52, 60, 68, 73, 81, 89, 94, 102, 107, 115, 123, 128, 136, 141, 149, 157, 162, 170, 178, 183, 191, 196, 204, 212, 217, 225, 233, 238, 246, 251, 259, 267, 272, 280, 285, 293, 301, 306, 314, 322, 327, 335, 340, 348, 356, 361, 369, 374, 382, 390, 395
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OFFSET
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1,1
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COMMENTS
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a(n)-3 are also the positions of 1 in A188436. - Federico Provvedi, Nov 22 2018
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LINKS
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Muniru A Asiru, Table of n, a(n) for n = 1..2000
J.-P. Allouche and F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424 [math.NT], 2018.
C. Kimberling, Complementary equations and Wythoff Sequences, JIS 11 (2008) 08.3.3.
Clark Kimberling, Intriguing infinite words composed of zeros and ones, Elemente der Mathematik (2021).
C. Kimberling and K. B. Stolarsky, Slow Beatty sequences, devious convergence, and partitional divergence, Amer. Math. Monthly, 123 (No. 2, 2016), 267-273.
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FORMULA
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a(n) = B(B(n)), n>=1, with B(k)=A001950(k) (Wythoff B-numbers). a(0)=0 with B(0)=0.
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MAPLE
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b:=n->floor(n*((1+sqrt(5))/2)^2): seq(b(b(n)), n=1..60); # Muniru A Asiru, Dec 05 2018
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MATHEMATICA
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b[n_] := Floor[n * GoldenRatio^2]; a[n_] := b[b[n]]; Array[a, 60] (* Amiram Eldar, Nov 22 2018 *)
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PROG
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(Python)
from sympy import S
for n in range(1, 60): print(int(S.GoldenRatio**2*(int(n*S.GoldenRatio**2))), end=', ') # Stefano Spezia, Dec 06 2018
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CROSSREFS
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Second row of A101858.
Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864.
Sequence in context: A120062 A081769 A188030 * A190432 A197563 A022138
Adjacent sequences: A101861 A101862 A101863 * A101865 A101866 A101867
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jan 28 2005
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STATUS
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approved
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