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A106730
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Product-based sequence of a Markov type based on a functional addition group.
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0
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2, 3, 0, 1, 3, 0, 1, 2, 4, 0, 1, 0, 1, 3, 4, 2, 3, 0, 1, 4, 4, 2, 3, 0, 1, 3, 0, 1, 2, 4, 4, 4, 0, 1, 4, 2, 2, 0, 1, 2, 2, 4, 4, 0, 1, 0, 1, 4, 4, 0, 1, 0, 1, 3, 4, 2, 3, 0, 1, 0, 1, 4, 2, 3, 3, 3, 2, 2, 0, 1, 4, 4, 3, 2, 4, 0, 1, 3, 4, 0, 1, 3, 0, 1, 0, 1, 4, 2, 0, 1, 2, 0, 1, 3, 4, 3, 4, 2, 4, 3, 2, 3, 3, 3, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The object of this sequence is to show a product Markov can be formed from an Addition group based on the primes. Modulo five can be taken as a signed modulo three: {0,1,2,3,4}->{-2,-1,0,-1,-2}
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FORMULA
| f(n)=10-Mod[Prime[n+3], 10] g[n]=Mod[Mod[n, 5], 4] h(n)]=g(f(n)) a(n)=Mod[Mod[(1+h[n))*a(n-1), 5]+1, 5]
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MATHEMATICA
| f[n_] = 10 - Mod[Prime[n + 3], 10] g[n_] = Mod[Mod[n, 5], 4] h[n_] = g[f[n]] digits = 20 aa[1] = 2; aa[n_] := aa[n] = Mod[Mod[aa[n - 1]*(1 + h[n]), 5] + 1, 5] c = Table[aa[n], {n, 1, digits^2/2}]
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CROSSREFS
| Sequence in context: A053645 A170899 A179392 * A089652 A112168 A072516
Adjacent sequences: A106727 A106728 A106729 * A106731 A106732 A106733
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 14 2005
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