|
|
A106533
|
|
The rumor constant: decimal expansion of the number x defined by x*e^(2 - 2*x) = 1.
|
|
9
|
|
|
2, 0, 3, 1, 8, 7, 8, 6, 9, 9, 7, 9, 9, 7, 9, 9, 5, 3, 8, 3, 8, 4, 7, 9, 0, 6, 2, 0, 6, 2, 4, 1, 9, 8, 7, 9, 1, 0, 5, 4, 9, 8, 7, 8, 7, 5, 9, 0, 5, 7, 0, 3, 1, 7, 5, 0, 0, 2, 4, 7, 7, 4, 4, 1, 5, 1, 9, 5, 7, 5, 0, 7, 5, 9, 1, 9, 0, 6, 0, 2, 4, 8, 8, 3, 6, 2, 5, 0, 3, 6, 1, 6, 9, 0, 7, 7, 9, 6, 4, 2, 9, 1, 4, 6, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
D. J. Daley and D. G. Kendall, Stochastic rumours, Journal of the Institute of Mathematics and Its Applications 1:42-55, 1965.
|
|
FORMULA
|
Solution to x*exp(2 - 2*x) = 1 with x not equal to 1.
Constant c satisfies: exp(c*x)/(1-2*c) = Sum_{n>=0} (x + 2*n)^n * exp(-2*n)/n!. - Paul D. Hanna, Mar 12 2016
|
|
EXAMPLE
|
c = 0.20318786997997995383847906206241987910549878759057031750024774...
|
|
MATHEMATICA
|
RealDigits[ -ProductLog[ -2/E^2]/2, 10, 111][[1]]
|
|
PROG
|
(PARI) solve(x=0, 0.5, x*exp(2-2*x)-1) \\ Michel Marcus, Mar 13 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|