A131213 Limiting trajectory of 1 under evenly-many applications of the morphism phi defined in the comments.

1, 3, 8, 13, 1, 5, 12, 13, 1, 8, 12, 14, 1, 2, 3, 4, 5, 6, 14, 1, 3, 8, 13, 3, 5, 10, 13, 3, 8, 10, 14, 1, 2, 3, 4, 5, 6, 14, 1, 3, 8, 13, 1, 8, 12, 14, 3, 8, 10, 14, 7, 8, 9, 10, 11, 12, 13, 2, 6, 7, 13, 1, 3, 8, 13, 2, 4, 9, 13, 3, 5, 10, 13, 4, 6, 11, 13, 1, 5, 12, 13, 7, 8, 9, 10, 11, 12, 13, 1

Offset

1,2

Comments

The morphism is based on the adjacencies between the 12 vertices and the two hexagonal face-centers of a hexagonal prism (see illustration):

phi(1) = {2, 6, 7, 13};

phi(2) = {1, 3, 8, 13};

phi(3) = {2, 4, 9, 13};

phi(4) = {3, 5, 10, 13};

phi(5) = {4, 6, 11, 13};

phi(6) = {1, 5, 12, 13};

phi(7) = {1, 8, 12, 14};

phi(8) = {2, 7, 9, 14};

phi(9) = {3, 8, 10, 14};

phi(10) = {4, 9, 11, 14};

phi(11) = {5, 10, 12, 14};

phi(12) = {6, 7, 11, 14};

phi(13) = {1, 2, 3, 4, 5, 6, 14};

phi(14) = {7, 8, 9, 10, 11, 12, 13}.

Links

Table of n, a(n) for n=1..89.

Michael Somos, Hexagonal prism in which the adjacencies give the morphism used in this sequence.

Index entries for sequences that are fixed points of mappings

Mathematica

Clear[s] s[1] = {2, 6, 7, 13}; s[2] = {1, 3, 8, 13}; s[3] = {2, 4, 9, 13}; s[4] = {3, 5, 10, 13}; s[5] = {4, 6, 11, 13}; s[6] = {1, 5, 12, 13}; s[7] = {1, 8, 12, 14}; s[8] = {2, 7, 9, 14}; s[9] = {3, 8, 10, 14}; s[10] = {4, 9, 11, 14}; s[11] = {5, 10, 12, 14}; s[12] = {6, 7, 11, 14}; s[13] = {1, 2, 3, 4, 5, 6, 14}; s[14] = {7, 8, 9, 10, 11, 12, 13}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[4]

Crossrefs

Sequence in context: A247396 A180507 A218889 * A320260 A105371 A038188

Adjacent sequences: A131210 A131211 A131212 * A131214 A131215 A131216

Keyword

nonn

Author

Roger L. Bagula, Sep 27 2007

Extensions

Edited by N. J. A. Sloane, Jan 24 2012 (But are 4 iterations enough to get the initial terms correctly? I would be happier if the Mma code ended with p[6] rather than p[4].)

Status

approved