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A156590
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Decimal expansion of the imaginary part of the limit of f(f(...f(0)...)) where f(z)=sqrt(i+z).
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1
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6, 2, 4, 8, 1, 0, 5, 3, 3, 8, 4, 3, 8, 2, 6, 5, 8, 6, 8, 7, 9, 6, 0, 4, 4, 4, 7, 4, 4, 2, 8, 5, 1, 4, 4, 4, 0, 0, 5, 2, 3, 4, 4, 5, 6, 4, 1, 9, 0, 0, 2, 3, 2, 7, 4, 7, 0, 1, 5, 4, 3, 1, 4, 6, 5, 3, 1, 7, 1, 0, 5, 5, 4, 3, 9, 4, 9, 6, 4, 0, 7, 0, 5, 2, 4, 5, 2, 8, 9, 1, 2, 7, 5, 5, 3, 2, 9, 5, 0, 9, 1, 7, 3, 1, 7
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The real part, 1.300242590..., is given by A156548.
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FORMULA
| Define z(1)=f(0)=sqrt(i), where i=sqrt(-1), and z(n)=f(z(n-1)) for n>1.
Write the limit of z(n) as a+bi where a and b are real. Then a=(b+1)/(2b),
where b=sqrt((sqrt(17)-1)/8).
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EXAMPLE
| 0.6248105338...
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CROSSREFS
| Cf. A156548.
Sequence in context: A125115 A202244 A020831 * A135617 A019930 A169843
Adjacent sequences: A156587 A156588 A156589 * A156591 A156592 A156593
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KEYWORD
| nonn,cons
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Feb 12 2009
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