OFFSET
1,1
COMMENTS
a(n) is the least number of random selections (with replacement) required that assures a group having at least a 0.5 probability of containing the top 100/(10^n)th percentile individual. Converges toward log(2)*10^n with increasing n.
REFERENCES
F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, 1965
FORMULA
a(n) = ceiling((log(2))/(log(10^n/(10^n-1)))).
EXAMPLE
To assure a greater than 1/2 chance of finding an individual with, say, an IQ in the top one out of a thousand or 1/(10^3), you must select at least (with replacement) a(3) = 693 individuals.
PROG
(PARI) a(n)=ceil((log(2))/(log(10^n/(10^n-1)))); \\ Joerg Arndt, Apr 15 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zacariaz Martinez, Apr 11 2013
STATUS
approved