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Search: id:A153112
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| A153112 |
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A cyclic collapsing ( Per Bak sand pile) recursion based on A004001: f(n)=If[Mod[ Floor[Sum[f(i), {i, 0, n - 1}]/2], 2^(4 + Mod[n, 3])] == 1, 1 + Mod[n, 3], f(f(n - 1)) + f(n - f(n - 1))]. |
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+0
3
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| 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 9, 10, 11, 2, 12, 12, 12, 13, 13, 2, 14, 14, 14, 14, 15, 16, 16, 17, 18, 18, 19, 19, 10, 19, 20, 20, 20, 21, 21, 21, 10, 24, 24, 13, 24, 25, 16, 26, 26, 26, 27, 27, 28, 28, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 2, 6, 7, 7, 8, 8, 8, 8, 5
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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It was a little difficult to get a scaling collapse recursion that maintained chaotic behavior in the Conway recursion.
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REFERENCES
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Per Bak, "How nature works, the science of self-organized criticality",Springer-Verlag, New York,1996,pages 49-64
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FORMULA
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f(n)=If[Mod[ Floor[Sum[f(i), {i, 0, n - 1}]/2], 2^(4 + Mod[n, 3])] == 1, 1 + Mod[n, 3], f(f(n - 1)) + f(n - f(n - 1))].
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MATHEMATICA
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Clear[f, n]; f[0] = 0; f[1] = 1; f[2] = 1;
f[n_] := f[n] = If[Mod[ Floor[Sum[f[i], {i, 0, n - 1}]/2], 2^(4 + Mod[n, 3])] == 1, 1 + Mod[n, 3],
f[f[n - 1]] + f[n - f[n - 1]]]; a = Table[f[n], {n, 0, 200}]
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CROSSREFS
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A004001, A092550, A136640
Sequence in context: A101646 A166079 A080677 this_sequence A005350 A055037 A125186
Adjacent sequences: A153109 A153110 A153111 this_sequence A153113 A153114 A153115
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 18 2008
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