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Search: id:A117875
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| A117875 |
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Semi-chaotic triangular array on the domain [0,8] made by Modulo 3 of A000045 added to Modulo 7 of A000045. |
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+0
1
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| 0, 1, 2, 1, 2, 2, 2, 3, 3, 4, 3, 4, 4, 5, 3, 5, 6, 6, 7, 5, 7, 1, 2, 2, 3, 1, 3, 3, 6, 7, 7, 8, 6, 8, 8, 7, 0, 1, 1, 2, 0, 2, 2, 1, 0, 6, 7, 7, 8, 6, 8, 8, 7, 6, 7, 6, 7, 7, 8, 6, 8, 8, 7, 6, 7, 7
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This sequence is a model of wave particle duality in Integer terms. The Modulos act as slits and the chaotic sequence that results has interfence patterns. The Integers behave in the Fibonacci sequence as if they were also continious. Thus quantum mechanics may apply to number theory and the theorems be useful in understanding such things as the primes. I am only here echoing men historically like Hilbert and Fourier.
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FORMULA
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a(n,m) =Mod[A000045[n],3]+Mod[A000045[m],7]
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EXAMPLE
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0
1, 2
1, 2, 2
2, 3, 3, 4
3, 4, 4, 5, 3
5, 6, 6, 7, 5, 7
1, 2, 2, 3, 1, 3, 3
6, 7, 7, 8, 6, 8, 8, 7
0, 1, 1, 2, 0, 2, 2, 1, 0
6, 7, 7, 8, 6, 8, 8, 7, 6, 7
6, 7, 7, 8, 6, 8, 8, 7, 6, 7, 7
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] f[n_, m_] := Mod[a[n], 3] + Mod[a[m], 7] aout = Table[Table[f[n, m], {n, 0, m}], {m, 0, 10}] c = Flatten[aout]
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CROSSREFS
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Cf. A000045.
Sequence in context: A029258 A070096 A024154 this_sequence A084840 A029278 A125950
Adjacent sequences: A117872 A117873 A117874 this_sequence A117876 A117877 A117878
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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), May 13 2006
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