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Search: id:A166493
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| 1, 1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 1, 7, 15, 12, 11, 14, 14, 12, 16, 16, 16, 16, 16, 20, 17, 17, 20, 11, 21, 25, 18, 20, 26, 22, 24, 19, 27, 17, 23, 30, 13, 28, 36, 24, 25, 32, 27, 30, 32, 28, 32, 36, 30, 32, 3, 50, 40, 22, 43, 31, 37, 35, 28, 40, 44, 33, 38, 49
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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This sequence shows two unique effects:
1) a break down to cyclic behavior three collapses in at about n=600
2) entropy plateau that correspond to the collapses:
e = Table[N[ -Log[f[n]/fm]*(f[n]/fm)], {n, 0, 1000}];
ListPlot[e, PlotJoined -> True, PlotRange -> All]
A153112 , the sand pile sequence based on A004001,
This plateau entropy effect is important because
it drives the self-organization in evolutionary processes
in biology. show the second effect, but no breakdown.
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MATHEMATICA
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Clear[f, n]; f[0] = 1; 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])] == 0,
1 + Mod[n, 3],
f[n - f[n - 1]] + f[n - f[n - 2]]];
a = Table[f[n], {n, 0, 200}]
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CROSSREFS
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Cf. A153112, A004001, A005185
Sequence in context: A094606 A080595 A123579 this_sequence A005185 A119466 A100922
Adjacent sequences: A166490 A166491 A166492 this_sequence A166494 A166495 A166496
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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), Oct 15 2009
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