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Search: id:A087721
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| A087721 |
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Strictly increasing domain of the Hofstadter batrachian sequence A005185. |
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+0
1
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| 2, 3, 4, 5, 6, 8, 10, 11, 12, 16, 20, 21, 22, 23, 24, 25, 30, 32, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 52, 54, 56, 58, 60, 61, 62, 64, 66, 68, 71, 72, 73, 77, 78, 79, 80, 82, 83, 85, 87, 88, 90, 91, 92, 93, 94, 96, 101, 106, 108, 109, 111, 114, 115, 118, 120, 122, 123
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This result came from discussion with Robert G. Wilson v about variations in chaotic sequences. The conclusion is that there are three distinct sets: 1) consecutive repeating 2) strictly increasing 3) strictly decreasing
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FORMULA
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a[n] =a[n - a[n-1]] + a[n - a[n-2]]
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MATHEMATICA
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digits=750 Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]] Hofstadter[1] = Hofstadter[2] = 1 a1=Table[Hofstadter[n], {n, 1, digits}]; f[x_, y_] := x-y/; x-y>0 f[x_, y_] := 0/; x-y<=0 b=Table[If[f[a1[[n]], a1[[n-1]]]>0, a1[[n]], 0], {n, 2, digits}]; c=Delete[Union[b], 1]
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CROSSREFS
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Cf. A005185, A087722, A087723.
Sequence in context: A070994 A057197 A067936 this_sequence A140642 A072666 A075471
Adjacent sequences: A087718 A087719 A087720 this_sequence A087722 A087723 A087724
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 29 2003
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