

A101864


Wythoff BB numbers.


21



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

1,1


COMMENTS

a(n)3 are also the positions of 1 in A188436.  Federico Provvedi, Nov 22 2018


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..2000
J.P. Allouche, 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
C. Kimberling and K. B. Stolarsky, Slow Beatty sequences, devious convergence, and partitional divergence, Amer. Math. Monthly, 123 (No. 2, 2016), 267273.


FORMULA

a(n) = B(B(n)), n>=1, with B(k)=A001950(k) (Wythoff Bnumbers). a(0)=0 with B(0)=0.


MAPLE

b:=n>floor(n*((1+sqrt(5))/2)^2): seq(b(b(n)), n=1..60); # Muniru A Asiru, Dec 05 2018


MATHEMATICA

b[n_] := Floor[n * GoldenRatio^2]; a[n_] := b[b[n]]; Array[a, 60] (* Amiram Eldar, Nov 22 2018 *)


PROG

(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


CROSSREFS

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


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jan 28 2005


STATUS

approved



