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A320084
Decimal expansion of solution of -x*log_2(x) - (1-x)*log_2(1-x) + (1-x)*log_2(3) = 1.
0
8, 1, 0, 7, 1, 0, 3, 7, 5, 0, 8, 4, 7, 6, 8, 2, 3, 7, 3, 9, 7, 6, 0, 5, 3, 0, 6, 6, 3, 4, 7, 2, 5, 7, 5, 7, 8, 3, 3, 0, 3, 3, 8, 3, 8, 1, 5, 6, 9, 5, 3, 6, 6, 1, 0, 7, 7, 9, 0, 9, 8, 3, 7, 8, 2, 3, 7, 8, 2, 4, 4, 9, 1, 5, 2, 6, 0, 0, 7, 1, 4, 2, 5, 2, 4, 4, 4, 8, 9, 0, 0, 1, 7, 7, 5, 5, 4, 2, 3, 1, 4, 8, 0, 4, 3, 5, 5
OFFSET
0,1
COMMENTS
Two people playing "online matching pennies" can get as close as they want to this fraction of success.
REFERENCES
Peter Winkler, "Mathematical Mind-Benders", ISBN 978-1-56881-336-3 (the number is given as "about 0.8016").
LINKS
Olivier Gossner, Penelope Hernandez, Abraham Neyman, Online Matching Pennies, 2003, Discussion Paper Series dp316, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
EXAMPLE
0.810710375084768237...
MAPLE
evalf(solve(-x*log[2](x)-(1-x)*log[2](1-x)+(1-x)*log[2](3)=1, x), 120); # Muniru A Asiru, Oct 05 2018
PROG
(PARI) solve(x=0.1, 0.9, -x*log(x) - (1-x)*log(1-x) + (1-x)*log(3) - log(2)); \\ Michel Marcus, Oct 06 2018
CROSSREFS
Sequence in context: A194732 A217739 A110544 * A153855 A340065 A011437
KEYWORD
nonn,cons
AUTHOR
Jack Zhang, Oct 05 2018
STATUS
approved