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A137419
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a(n) = (a(n - 4) + 1 - ((-1)^a(a(n - 1)) + 1)*(a(a(n - 1)) - a(a(n - 2)))/2).
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0
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1, 2, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 3, 4, 5, 3, 4, 5, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 8, 7, 8, 8, 9, 8, 10, 9, 10, 9, 11, 9, 11, 9, 12, 10, 12, 10, 13, 11, 12, 11, 13, 12, 13, 12, 14, 12, 14, 12, 15, 13, 15, 13, 16, 14, 15, 14, 18, 15, 16, 15, 19, 16, 17, 15, 20, 18, 18, 16, 21, 19, 19, 17, 23
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A recursive chaotic sequence based on Bertran Steinsky's sequence.
I started with the sequence from Bertran Steinsky quoted in A000002:
a[1] = 1; a[2] = 2; a[3] = 2;
a[n_] := a[n] = a[n - 1] + 1 - ((-1)^a[a[n - 1]] + 1)*(a[n - 1] - a[n - 2])/2;
and worked to minimize it while getting a more chaotic result.
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REFERENCES
| Bertran Steinsky, A Recursive Formula for the Kolakoski Sequence A000002, J. Integer Sequences, Vol. 9 (2006), Article 06.3.7.
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FORMULA
| a(1) = 1; a(2) = 2; a(3) = 2; a(4) = 1; a(n) = (a(n - 4) + 1 - ((-1)^a(a(n - 1)) + 1)*(a(a(n - 1)) - a(a(n - 2)))/2)
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MATHEMATICA
| Clear[a] a[1] = 1; a[2] = 2; a[3] = 2; a[4] = 1; a[n_] := a[n] = (a[n - 4] + 1 - ((-1)^a[a[n - 1]] + 1)*(a[a[n - 1]] - a[a[n - 2]])/2); Table[a[n], {n, 1, 100}]
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CROSSREFS
| Cf. A000002.
Sequence in context: A029286 A050333 A143999 * A057536 A014420 A029289
Adjacent sequences: A137416 A137417 A137418 * A137420 A137421 A137422
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 21 2008
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