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A156548
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Decimal expansion of the real part of the limit of f(f(...f(0)...)) where f(z)=sqrt(i+z).
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1
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1, 3, 0, 0, 2, 4, 2, 5, 9, 0, 2, 2, 0, 1, 2, 0, 4, 1, 9, 1, 5, 8, 9, 0, 9, 8, 2, 0, 7, 4, 9, 5, 2, 1, 3, 8, 8, 5, 4, 8, 5, 3, 2, 8, 1, 9, 1, 8, 3, 9, 4, 7, 6, 1, 0, 1, 0, 4, 8, 3, 6, 1, 4, 0, 7, 5, 2, 8, 1, 2, 8, 0, 3, 4, 9, 9, 1, 3, 6, 3, 8, 1, 5, 0, 8, 9, 1, 0, 2, 8, 3, 4, 1, 3, 4, 2, 1, 9, 4, 6, 6, 4, 8, 2, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The imaginary part, 0.624810..., is given by A156590.
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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
| 1.300242590220...
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CROSSREFS
| Cf. A156590.
Sequence in context: A128113 A108930 A059682 * A112883 A117138 A095104
Adjacent sequences: A156545 A156546 A156547 * A156549 A156550 A156551
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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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