Mike Croucher asked the following question on his blog. Suppose you draw M sequences of random numbers of length N from a random number generator. What is the probability that they will overlap?
Assumes your random number generator is a cyclical list of p unique integers. Each draw picks a random starting point in the cycle [...]
A detailed comparison of DNA and RNA in human cells has uncovered a surprising number of cases where the corresponding sequences are not, as has long been assumed, identical. The RNA-DNA differences generate proteins that do not pre... Read Post
Here's a problem that occurred to me yesterday: consider a sequence of real numbers a 0, a 1, a 2,.... Let b k = (a 0 + a 1 +... + a k )/(k+1) be the average of the first (k+1) of the a i. When is a sequence equal to its own sequenc... Read Post