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Search: id:A091808
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| A091808 |
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Given the infinite continued fraction i+(i/(i+(i/(i+...)))), where i is the square root of (-1), this is the numerator of the imaginary part of the convergents. |
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+0
7
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| 1, 1, 3, 6, 4, 13, 53, 111, 231, 160, 1000, 13, 4329, 693, 2083, 39014, 81188, 84477, 351597
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The sequence of complex numbers (which this sequence is part of) converges to (i+sqrt(-1+4i))/2, found by simply solving the equation A=i+(i/A) for A using the quadratic formula. When plotted in the complex plane, these numbers form a counter-clockwise spiral that quickly converges to a point.
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EXAMPLE
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a(6)=13 since the sixth convergent is (3/5)+(13/10)i and hence the numerator of the imaginary part is 13.
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MATHEMATICA
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GenerateA091808[1] := I; GenerateA091808[n_] := I + I/(GenerateA091808[n-1]); GenerateNumeratorsA091808[n_] := Table[Numerator[Im[GenerateA091808[x]]], {x, 1, n}]; GenerateNumeratorsA091808[20] would give the first 20 terms.
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CROSSREFS
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Cf. A091806-A091809.
Sequence in context: A122634 A098383 A067979 this_sequence A128719 A009782 A016615
Adjacent sequences: A091805 A091806 A091807 this_sequence A091809 A091810 A091811
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KEYWORD
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cofr,frac,nonn
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AUTHOR
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Ryan Witko (witko(AT)nyu.edu), Mar 06 2004
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