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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 05:06 EDT 2021. Contains 343688 sequences. (Running on oeis4.)