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Search: id:A037905
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| A037905 |
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a(n) = 9 - (floor(n*Pi) mod 9). |
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+0
1
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| 6, 3, 9, 6, 3, 9, 6, 2, 8, 5, 2, 8, 5, 2, 7, 4, 1, 7, 4, 1, 7, 3, 9, 6, 3, 9, 6, 3, 8, 5, 2, 8, 5, 2, 8, 4, 1, 7, 4, 1, 7, 4, 9, 6, 3, 9, 6, 3, 9, 5, 2, 8, 5, 2, 8, 5, 1, 7, 4, 1, 7, 4, 1, 6, 3, 9, 6, 3, 9, 6, 2, 8, 5, 2, 8, 5, 2, 7, 4, 1, 7, 4, 1, 7, 3, 9, 6, 3, 9, 6, 3, 8, 5, 2, 8, 5, 2, 8, 4, 1, 7, 4, 1, 7, 4
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A Beatty conjugate modulo 9 of the Pi irrational rotation.
What is unique about this sequence is that it can be broken up into nine "orthogonal" binary sequences. It also determines a unique irrational number that is very probably a transcendental number as well.
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FORMULA
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f[n_]=9-Mod[Floor[n*Pi], 9]
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EXAMPLE
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9-mod[Floor[1*Pi],9]=9-3=6, 9-modFloor[2*Pi],9]=9-6=3, 9-mod[Floor[3*Pi],9]=9-0=9, etc.
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MATHEMATICA
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f[n_] := 9 - Mod[Floor[n*\[Pi]], 9]; Table[f[n], {n, 1, 105}] (* OR *)
fn[x_, y_] := Which[9 - Mod[Floor[n*\[Pi]], 9] == y, y, True, 0]; an[y_] := N[Sum[fn[n, y]*10^(-n), {n, 1, 200}], 200]; Sum[ an[i], {i, 1, 9}]
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CROSSREFS
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Sequence in context: A021065 A093754 A135935 this_sequence A154465 A147313 A066070
Adjacent sequences: A037902 A037903 A037904 this_sequence A037906 A037907 A037908
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 27 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2002
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