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Search: id:A116566
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| A116566 |
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Chaotic Matrix Markov based on Ono supersingular polynomial as characteristic function. |
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+0
1
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| 1, 1, 28, 31, 13, 22, 24, 28, 7, 10, 18, 23, 26, 23, 24, 28, 18, 4, 9, 18, 22, 29, 13, 20, 30, 8, 36, 14, 35, 13, 36, 20, 6, 5, 32, 13, 33, 29, 13, 30, 1, 20, 18, 7, 27, 3, 22, 4, 13, 6
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This is characteristic polynomial of the paper's example: S37[x] =Mod[Expand[(x + 29)*(x^2 + 31*x + 31)], 37] Roots modulo 37 are: Table[Mod[x /. NSolve[Det[M - IdentityMatrix[3]*x] == 0, x][[n]], 37], {n, 1, 3}] {25.1149, 35.9627, 35.9224}
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REFERENCES
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Ken Ono and Scott Ahlgren, Weierstrass points on X0(p) and supersingular j-invariants Mathematiche Annalen 325, 2003, pp. 355-368
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FORMULA
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M = {{0, 1, 0}, {0, 0, 1}, {899, 930, 60}} w[0] = {0, 1, 1}; w[n_] := w[n] = M.w[n - 1] a(n) =Mod[w[n][[1]],37]
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MATHEMATICA
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M = {{0, 1, 0}, {0, 0, 1}, {899, 930, 60}} Det[M - IdentityMatrix[3]*x] NSolve[Det[M - IdentityMatrix[3]*x] == 0, x] w[0] = {0, 1, 1}; w[n_] := w[n] = M.w[n - 1] a0 = Table[Mod[w[n][[1]], 37], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A054396 A083274 A067913 this_sequence A057483 A025367 A031171
Adjacent sequences: A116563 A116564 A116565 this_sequence A116567 A116568 A116569
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KEYWORD
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nonn,uned,probation,obsc
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 17 2006
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