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Search: id:A137178
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| A137178 |
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a(n) = sum_(1..n) [S2(n)mod 2 - floor(5*S2(n)/7)mod 2], where S2(n) = binary weight of n. |
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1
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| 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 2, 3, 2, 1, 2, 1, 2, 3, 3, 2, 3, 4, 4, 5, 5, 5, 5, 6, 5, 4, 5, 4, 5, 6, 6, 5, 6, 7, 7, 8, 8, 8, 8, 7, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 11, 10, 11, 10, 11, 12, 12, 11, 12, 13, 13, 14, 14, 14, 14, 13, 14, 15, 15, 16, 16, 16
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The graph of this sequence is a special case of de Rham's fractal curve. In general, the graph of any sequence of the form a(n)=sum_(1..n) [Sk(n)mod m - floor(p*Sk(n)/q)mod m], where Sk(n) is the digit sum of n, n in k-ary notation, p,q,m integers, gives a de Rham fractal curve. The self-symmetries of all of de Rham curves are given by the monoid that describes the symmetries of the infinite binary tree or Cantor set. This so-called period-doubling monoid is a subset of the modular group.
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REFERENCES
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John A. Pelesko, Generalizing the Conway-Hofstadter $10,000 Sequence, Article 04.3.52; Journal of Integer Sequences, Vol. 7 (2004).
Klaus Pinn, Order and Chaos in Hofstadter's Q(n) Sequence, http://arXiv.org/PS_cache/chao-dyn/pdf/9803/9803012v2.pdf
Klaus Pinn, A Chaotic Cousin Of Conway's Recursive Sequence, http://arXiv.org/PS_cache/cond-mat/pdf/9808/9808031v1.pdf
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CROSSREFS
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Cf. A005185, A010060, A115384, A135585, A135947, A135993, A004001, A004526, A004396, A037915, A135133, A135136.
Sequence in context: A060588 A102565 A076826 this_sequence A101666 A035224 A130911
Adjacent sequences: A137175 A137176 A137177 this_sequence A137179 A137180 A137181
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Apr 04 2008, Apr 15 2008
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