A059129 A hierarchical sequence (W2{2}* - see A059126).

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, 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, 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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..104.

Jonas Wallgren, Hierarchical sequences

E. D. Demaine, M. L. Demaine, Y. N. Minsky, J. S. B. Mitchell, R. L. Rivest, and M. Patrascu, Picture-Hanging Puzzles, arXiv:1203.3602, [cs.DS], 2012-2014.

Crossrefs

Cf. A034947, A059126.

Sequence in context: A105203 A317952 A059131 * A349954 A081771 A338170

Adjacent sequences: A059126 A059127 A059128 * A059130 A059131 A059132

Keyword

easy,nonn

Author

Jonas Wallgren, Jan 19 2001

Status

approved