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A134864
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Wythoff BBB numbers.
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11
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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
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OFFSET
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1,1
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COMMENTS
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The lower and upper Wythoff sequences, A and B, satisfy the complementary equation BBB=3A+5B.
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LINKS
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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.
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FORMULA
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a(n) = B(B(B(n))), n>=1, with B=A001950, the upper Wythoff sequence.
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MAPLE
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a:=n->floor(n*((1+sqrt(5))/2)^2): [a(a(a(n)))$n=1..55]; # Muniru A Asiru, Nov 24 2018
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Nov 14 2007
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STATUS
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approved
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