A102268 Decimal expansion of inverse binary entropy function of 1/2.

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

Offset

0,5

References

Fano, Robert M., Transmission of Information, M.I.T. Press, Cambridge, Mass.; John Wiley & Sons, Inc., New York-London, 1961.

Links

Table of n, a(n) for n=0..98.

Formula

Solution to h(x) = -x log_2 (x) - (1-x) log_2 (1-x) = 1/2.

Example

0.1100278644383595512618117...

Mathematica

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 *)

Crossrefs

Sequence in context: A141721 A129603 A263809 * A155062 A021786 A256514

Adjacent sequences: A102265 A102266 A102267 * A102269 A102270 A102271

Keyword

nonn,cons

Author

N. J. A. Sloane, Feb 19 2005

Status

approved