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A131213
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Limiting trajectory of 1 under evenly-many applications of the morphism phi defined in the comments.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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}.
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LINKS
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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
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A247396 A180507 A218889 * A320260 A105371 A038188
Adjacent sequences: A131210 A131211 A131212 * A131214 A131215 A131216
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula, Sep 27 2007
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EXTENSIONS
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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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STATUS
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approved
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