|
|
A200439
|
|
Decimal expansion of constant arising in clubbed binomial approximation for the lightbulb process.
|
|
0
|
|
|
2, 7, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
In the so-called lightbulb process, on days r = 1, ..., n, out of n lightbulbs, all initially off, exactly r bulbs selected uniformly and independent of the past have their status changed from off to on, or vice versa. With W_n the number of bulbs on at the terminal time n and C_n a suitable clubbed binomial distribution, d_{TV}(W_n,C_n) <= 2.7314 sqrt{n} e^{-(n+1)/3} for all n >= 1.
This is the value of the function g_1(9) after eq (16) of the preprint.
|
|
LINKS
|
|
|
EXAMPLE
|
2.731313... = 1352/495.
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|