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 A131213 Limiting trajectory of 1 under evenly-many applications of the morphism phi defined in the comments. 4

%I

%S 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,

%T 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,

%U 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

%H Michael Somos, <a href="/A131213/a131213.png">Hexagonal prism in which the adjacencies give the morphism used in this sequence.</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%t 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]

%K nonn

%O 1,2

%A _Roger L. Bagula_, Sep 27 2007

%E 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].)

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)