A059129 - OEIS

%I #23 Feb 18 2023 08:10:20

%S 1,2,1,2,3,2,1,2,1,3,4,3,1,2,1,2,3,2,1,2,1,4,5,4,1,2,1,2,3,2,1,2,1,3,

%T 4,3,1,2,1,2,3,2,1,2,1,5,6,5,1,2,1,2,3,2,1,2,1,3,4,3,1,2,1,2,3,2,1,2,

%U 1,4,5,4,1,2,1,2,3,2,1,2,1,3,4,3,1,2,1,2,3,2,1,2,1,6,7,6,1,2,1,2,3,2,1,2,1

%N A hierarchical sequence (W2{2}* - see A059126).

%C Begin with the empty finite sequence s_0. Inductively extend s_n to obtain s_{n+1} as follows: if s_n is given by a, b, c, ..., d, e, f, with g being the least integer that is not a value of s_n, then s_{n+1} is a, b, c, ..., d, e, f, g, -f, -e, -d, ..., -c, -d, -a, -g. The terms of {a(n)} give the absolute values of the limit of these sequences. These finite sequences naturally describe elements of fundamental groups occurring in picture-hanging puzzles and Brunnian links. - _Thomas Anton_, Oct 15 2022

%H Jonas Wallgren, <a href="/A059126/a059126.txt">Hierarchical sequences</a>

%H E. D. Demaine, M. L. Demaine, Y. N. Minsky, J. S. B. Mitchell, R. L. Rivest, and M. Patrascu, <a href="https://arxiv.org/abs/1203.3602">Picture-Hanging Puzzles</a>, arXiv:1203.3602, [cs.DS], 2012-2014.

%Y Cf. A034947, A059126.

%K easy,nonn

%O 0,2

%A _Jonas Wallgren_, Jan 19 2001