

A117610


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}.


0



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
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OFFSET

0,1


COMMENTS

This method was a difficult model to program: it bifurcated 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.


LINKS

Table of n, a(n) for n=0..71.


FORMULA

v[n]=vector v[n1] permutated by Matrix M[n] a(n+m1) =v[n][[m]]


MATHEMATICA

(*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 switches 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}]]


CROSSREFS

Sequence in context: A193301 A213250 A226689 * A176173 A200327 A206546
Adjacent sequences: A117607 A117608 A117609 * A117611 A117612 A117613


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula, Apr 06 2006


STATUS

approved



