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Search: id:A117610
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| A117610 |
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A Matrix Markov based on solved permutation Matrices Modulo 15 as 8 X 8 matrices extracted from the primes relative to the first set of eight primes free of {3,5}. |
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1
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| 7, 11, 13, 2, 4, 8, 14, 1, 11, 13, 2, 8, 14, 1, 7, 11, 2, 14, 1, 7, 11, 13, 2, 8, 11, 13, 2, 14, 7, 11, 2, 8, 11, 2, 14, 11, 2, 8, 13, 2, 11, 2, 2, 14, 11, 2, 8, 13, 13, 2, 14, 2, 8, 13, 11, 2, 14, 13, 13, 2, 14, 2, 2, 13, 13, 13, 2, 14, 2, 2, 13, 14
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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This method was a difficult model to program: it bifucated at higher iterations to gives mostly {2,13,14} leaving out the other values. Observationally in terms of the modulo 10 endings {1,3,7,9} the modulo 15 ending pair as: 1 --> {1,11},3 --> {8,13},7 --> {2,7},9 --> {4,14} The idea is that an elliptically polarized partitioning of the primes should behave as permutation of these eight modulo 15 endings.
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FORMULA
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v[n]=vector v[n-1] permutated by Matrix M[n] a(n+m-1) =v[n][[m]]
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MATHEMATICA
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(*a-> Prime[4]to Prime[12 modulo 15 as the reference sequence*) a = {7, 11, 13, 2, 4, 8, 14, 1}; (* finds permutations of the reference sequence to match the actual primes*) M = Table[Table[If[Mod[Prime[i + n], 15] - a[[m]] == 0, 1, 0], {n, 1, 8}, {m, 1, 8}], {i, 4, 68, 8}]; (* matrix Markov sqwitches the permutation matrics in order*) v[0] = a; v[n_] := v[n] = M[[1 + Mod[n, 8]]].v[n - 1] a0 = Flatten[Table[v[n][[m]], {n, 0, 8}, {m, 1, 8}]]
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CROSSREFS
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Sequence in context: A054510 A134702 A053674 this_sequence A084451 A091901 A072823
Adjacent sequences: A117607 A117608 A117609 this_sequence A117611 A117612 A117613
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 06 2006
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