A135993 -id:A135993 - cp's OEIS frontend

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

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

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.

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.

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

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

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

cp's OEIS Frontend

A137178 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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