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Search: id:A086267
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| A086267 |
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A quantum energy sequence from Hofstadter's sequence. |
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+0
2
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| 1, 0, 2, 5, 4, 5, 7, 7, 2, 2, 2, 4, 4, 4, 6, 5, 6, 7, 7, 2, 2, 3, 2, 6, 4, 4, 6, 6, 7, 6, 4, 7, 7, 4, 5, 3, 4, 6, 5, 6, 7, 7, 2, 2, 2, 3, 2, 5, 3, 3, 2, 7, 4, 2, 3, 6, 5, 2, 4, 4, 5, 4, 7, 6, 3, 4, 8, 5, 5, 7, 3, 4, 6, 5, 7, 5, 2, 6, 7, 3, 4, 3, 3, 6, 4, 5, 7, 7, 6, 2, 2, 2, 2, 3, 2, 7, 7, 6, 2, 5, 2, 2, 3, 4, 3
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This energy formulation seems to work for modulo 5 and 6 at digits=500 levels.
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FORMULA
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Hofstadter[n] =Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]]
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MATHEMATICA
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Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]] Hofstadter[1] = Hofstadter[2] = 1 Digits=502 a=Table[Hofstadter[n], {n, 1, Digits}]; b=Table[Floor[(a[[n]]-2*a[[n+1]]+a[[n+2]]-4)/a[[n]]]+Mod[a[[n]], 6]+3, {n, 1, Digits-2}] ListPlot[b]
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CROSSREFS
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Sequence in context: A102066 A072970 A011036 this_sequence A053424 A163809 A075771
Adjacent sequences: A086264 A086265 A086266 this_sequence A086268 A086269 A086270
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KEYWORD
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nonn,obsc,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 28 2003
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EXTENSIONS
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I do not understand the definition of this sequence. - N. J. A. Sloane (njas(AT)research.att.com).
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