# Problem 316: Numbers in decimal expansions
Let p = p1 p2 p3 ... be an infinite sequence of random digits, selected
from {0,1,2,3,4,5,6,7,8,9} with equal probability. It can be seen that p
corresponds to the real number 0.p1 p2 p3 .... It can also be seen that
choosing a random real number from the interval \[0,1) is equivalent to
choosing an infinite sequence of random digits selected from
{0,1,2,3,4,5,6,7,8,9} with equal probability. For any positive integer n
with d decimal digits, let k be the smallest index such that pk, pk+1,
...pk+d-1 are the decimal digits of n, in the same order. Also, let g(n)
be the expected value of k; it can be proven that g(n) is always finite
and, interestingly, always an integer number. For example, if n = 535,
then for p = 31415926535897...., we get k = 9 for p =
355287143650049560000490848764084685354..., we get k = 36 etc and we
find that g(535) = 1008. Given that , find Note: represents the floor
function.