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A102268
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Decimal expansion of inverse binary entropy function of 1/2.
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0
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1, 1, 0, 0, 2, 7, 8, 6, 4, 4, 3, 8, 3, 5, 9, 5, 5, 1, 2, 6, 1, 8, 1, 1, 7, 0, 4, 3, 3, 4, 9, 8, 9, 4, 6, 0, 1, 7, 7, 1, 1, 4, 9, 0, 5, 0, 9, 1, 8, 9, 4, 9, 3, 4, 2, 8, 0, 6, 8, 0, 8, 1, 1, 0, 6, 4, 2, 7, 9, 8, 7, 3, 8, 1, 2, 8, 4, 8, 5, 1, 1, 2, 9, 6, 4, 2, 9, 8, 0, 2, 6, 6, 6, 5, 9, 1, 2, 9, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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REFERENCES
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Fano, Robert M., Transmission of Information, M.I.T. Press, Cambridge, Mass.; John Wiley & Sons, Inc., New York-London, 1961.
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LINKS
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FORMULA
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Solution to h(x) = -x log_2 (x) - (1-x) log_2 (1-x) = 1/2.
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EXAMPLE
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0.1100278644383595512618117...
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MATHEMATICA
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x /. FindRoot[ -x*Log[x] - (1-x)*Log[1-x] == Log[2]/2 , {x, 1/10}, WorkingPrecision -> 99] // RealDigits // First (* Jean-François Alcover, Mar 07 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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