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A141030
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A double prime irrational rotation sequence: a(n)=If[Prime[n + 1]^2 - Prime[n]*Prime[n + 2] > 0, If[Mod[Prime[n]*Sqrt[5], 1] >= 0.5, 0, 1], If[Mod[Prime[n]*Sqrt[7], 1] >= 0.5, 2, 3]].
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0
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3, 0, 3, 0, 3, 1, 2, 3, 1, 2, 1, 0, 3, 2, 1, 0, 3, 1, 0, 2, 1, 3, 2, 1, 0, 3, 1, 3, 3, 0, 3, 0, 3, 0, 3, 0, 1, 3, 1, 0, 2, 0, 3, 0, 3, 0, 0, 0, 2, 2, 1, 3, 0, 1, 0, 1, 2, 0, 1, 3, 2, 1, 1, 2, 3, 0, 2, 0, 3, 3, 2, 0, 0, 1, 2, 3, 0, 3, 2, 0, 2, 1, 3, 1, 3, 3, 0, 0, 2, 2, 1, 1, 3, 0, 3, 2, 1, 3, 1, 3
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A sequence designed to use the behavior of good and bad primes and the irrational rotation of primes square roots to give a four symbol {0,1,2,3} chaotic sequence
that is deterministic. The idea is that this would simulate the behavior of
the zeta zero complex part b[n]:
Zeta[1/2+I*b[n]]=0;
where:
a(n)~b[n]*Log[Prime[n]]/(Pi^2*n).
The sequence is definitely chaotic, but I don't know how successful at the simulation.
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FORMULA
| a(n)=If[Prime[n + 1]^2 - Prime[n]*Prime[n + 2] > 0, If[Mod[Prime[n]*Sqrt[5], 1] >= 0.5, 0, 1], If[Mod[Prime[n]*Sqrt[7], 1] >= 0.5, 2, 3]].
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MATHEMATICA
| Clear[f, n, a] f[n_] = If[Prime[n + 1]^2 - Prime[n]*Prime[n + 2] > 0, If[Mod[Prime[n]*Sqrt[5], 1] >= 0.5, 0, 1], If[Mod[Prime[n]*Sqrt[7], 1] >= 0.5, 2, 3]]; a = Table[f[n], {n, 1, 100}]
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CROSSREFS
| Cf. A046869.
Sequence in context: A010674 A021037 A053387 * A194084 A100258 A045763
Adjacent sequences: A141027 A141028 A141029 * A141031 A141032 A141033
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 30 2008
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