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 A134864 Wythoff BBB numbers. 11
 13, 34, 47, 68, 89, 102, 123, 136, 157, 178, 191, 212, 233, 246, 267, 280, 301, 322, 335, 356, 369, 390, 411, 424, 445, 466, 479, 500, 513, 534, 555, 568, 589, 610, 623, 644, 657, 678, 699, 712, 733, 746, 767, 788, 801, 822, 843, 856, 877, 890, 911, 932, 945 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BBB=3A+5B. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..5000 Clark Kimberling, Complementary equations and Wythoff Sequences, Journal of Integer Sequences 11 (2008) Article 08.3.3. FORMULA a(n) = B(B(B(n))), n>=1, with B=A001950, the upper Wythoff sequence. MAPLE a:=n->floor(n*((1+sqrt(5))/2)^2): [a(a(a(n)))\$n=1..55]; # Muniru A Asiru, Nov 24 2018 MATHEMATICA Nest[Quotient[#(3+Sqrt@5), 2]&, #, 3]&/@Range@100 (* Federico Provvedi, Nov 24 2018 *) b[n_]:=Floor[n GoldenRatio^2]; a[n_]:=b[b[b[n]]]; Array[a, 60] (* Vincenzo Librandi, Nov 24 2018 *) PROG (Python) from sympy import floor from mpmath import phi def B(n): return floor(n*phi**2) def a(n): return B(B(B(n))) # Indranil Ghosh, Jun 10 2017 CROSSREFS Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134859, A035337, A134860, A134861, A134862, A035338, A134863, A035513. 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. Sequence in context: A124659 A164539 A245170 * A093100 A292472 A081271 Adjacent sequences:  A134861 A134862 A134863 * A134865 A134866 A134867 KEYWORD nonn AUTHOR Clark Kimberling, Nov 14 2007 STATUS approved

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Last modified June 26 18:18 EDT 2022. Contains 354885 sequences. (Running on oeis4.)