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A132150
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Semi-chaotic Jazz function (Oscar Peterson robot function) on 13 tones: a[n]->a[n-1]+/- 3 or 4 without 5 and 10 modulo 13.
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1
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4, 11, 1, 7, 3, 3, 11, 4, 7, 1, 9, 9, 4, 11, 1, 7, 2, 3, 11, 4, 7, 13, 8, 9, 4, 9, 13, 6, 1, 2, 9, 3, 6, 12, 7, 8, 3, 9, 12, 4, 13, 1, 9, 2, 4, 11, 6, 7, 2, 8, 11, 4, 12, 13, 8, 1, 4, 9, 4, 6, 1, 7, 9, 3, 11, 12, 7, 13, 3, 9, 4, 4, 13, 6, 9, 2, 9, 11, 6, 12, 2, 8, 3, 4, 12, 4, 8, 1, 9, 9, 4, 11, 1, 7, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Mixing the audio from this function with Oscar Peterson recordings doesn't produce any major length discords: sounds like a Jazz session.
For n >= 13, a(n) is periodic with period 78. - Robert Israel, Feb 24 2017
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LINKS
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FORMULA
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Plus or minus 3 or 4: f(x)= x + 3*(2*Mod[x, 3] - 1) + Mod[x, 2]; Modulo 13: g(x)= If[f(x) > 12, 1 + Mod[f(x), 13], f(x)]; Modulo 5 equals zero removed: h(x) = If[Mod[g(x), 5] == 0, g(x) - 1, g(x)] a(n) = h(n).
Let f(n) = n + p(n) where p is periodic with period 6, values 4, 9, -2, 3, 10, -3 for n=1..6.
Let g(n) = 1 + (f(n) mod 13) if f(n) > 12, else g(n) = f(n).
Then a(n) = g(n) - 1 if g(n) == 0 (mod 5), else a(n) = g(n).
G.f.: x*(4 +7*x -10*x^2 +6*x^3 -4*x^4 +12*x^6 -7*x^8 +4*x^10 +7*x^12 +7*x^13 -17*x^14 +6*x^15 -x^16 +x^17 +15*x^18 -14*x^20 +12*x^21 -6*x^22 +2*x^23 +10*x^24 +5*x^25 -10*x^26 +5*x^27 -11*x^28 +3*x^29 +17*x^30 -x^31 -7*x^32 +11*x^33 -16*x^34 +4*x^35 +12*x^36 +5*x^37 -4*x^38 +3*x^39 -7*x^40 -8*x^41 +20*x^42 -2*x^43 -2*x^44 +10*x^45 -12*x^46 -7*x^47 +15*x^48 +4*x^49 +x^50 +3*x^51 -4*x^52 -6*x^53 +10*x^54 -3*x^55 +4*x^56 +8*x^57 -9*x^58 -4*x^59 +5*x^60 +3*x^61 +6*x^62 +2*x^63 -x^64 -3*x^65 +9*x^67 -4*x^68 +8*x^69 -6*x^70 -3*x^71 +9*x^72 +2*x^73 -x^74 +x^75 +x^76 -x^77 +x^79 -x^80 +x^81) / (1 -x +x^6 -x^7 +x^12 -x^13 +x^18 -x^19 +x^24 -x^25 +x^30 -x^31 +x^36 -x^37 +x^42 -x^43 +x^48 -x^49 +x^54 -x^55 +x^60 -x^61 +x^66 -x^67 +x^72 -x^73).
(End)
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MAPLE
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F:= [seq(x+3*(2*(x mod 3)-1) + (x mod 2), x=1..300)]:
G:= map(t -> if t > 12 then 1 + (t mod 13) else t fi, F):
map(t -> if t mod 5 = 0 then t-1 else t fi, G); # Robert Israel, Feb 24 2017
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MATHEMATICA
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f[x_] := x + 3*(2*Mod[x, 3] - 1) + Mod[x, 2]; g[x_] := If[f[x] > 12, 1 + Mod[f[x], 13], f[x]]; h[x_] := If[Mod[g[x], 5] == 0, g[x] - 1, g[x]]; a = Table[h[x], {x, 1, 256}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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