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, 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

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