

A141030


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]].


0



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
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OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..100.


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]].


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}]


CROSSREFS

Cf. A046869.
Sequence in context: A053387 A221170 A307199 * A221168 A194084 A262281
Adjacent sequences: A141027 A141028 A141029 * A141031 A141032 A141033


KEYWORD

nonn,uned,tabl


AUTHOR

Roger L. Bagula, Jul 30 2008


STATUS

approved



