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A137178 a(n) = sum_(1..n) [S2(n)mod 2 - floor(5*S2(n)/7)mod 2], where S2(n) = binary weight of n. 0
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; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..86.

John A. Pelesko, Generalizing the Conway-Hofstadter $10,000 Sequence, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.5.

Klaus Pinn, Order and Chaos in Hofstadter's Q(n) Sequence, arXiv:chao-dyn/9803012, 1998.

Klaus Pinn, A Chaotic Cousin Of Conway's Recursive Sequence, arXiv:cond-mat/9808031, 1998.

MATHEMATICA

Accumulate@ Array[Mod[#2, 2] - Mod[Floor[5 #2/7], 2] & @@ {#, DigitCount[#, 2, 1]} &, 85, 0] (* Michael De Vlieger, Jan 23 2019 *)

CROSSREFS

Cf. A005185, A010060, A115384, A135585, A135947, A135993, A004001, A004526, A004396, A037915, A135133, A135136.

Sequence in context: A272356 A102565 A076826 * A101666 A035224 A272677

Adjacent sequences:  A137175 A137176 A137177 * A137179 A137180 A137181

KEYWORD

easy,nonn

AUTHOR

Ctibor O. Zizka, Apr 04 2008, Apr 15 2008

EXTENSIONS

Converted references to links - R. J. Mathar, Oct 30 2009

STATUS

approved

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Last modified April 23 18:15 EDT 2019. Contains 322387 sequences. (Running on oeis4.)