The following are the smallest 9 elements of an infinite set of integers:

0,1,5,6,25,76,376,625,9376

What rule generates the set? What are the next two values?

There looks to be a link relating to powers of 5...

0 = 0*(5^0)
1 = 0*(5^0) + 1 = 5^0
5 = 1*(5^1)
6 = 1*(5^1) + 1
Looking good in terms of a pattern, but then we get...
25 = 1*(5^2)
76 = 3*(5^2) + 1
376 = 3*(5^3) + 1
625 = 1*(5^4) = 5*(5^3)
9376 = 3*(5^5) + 1 = 3*5*(5^4) + 1

The question does state that the numbers are the'smallest' 9 elements, which does not necessarily mean that they are the 'first' 9 elements. So if the rule sequentially generates increases and decreases in the numbers, then it follows that the first 9 numbers generated by the rule are not necessarily those in the question.

From here I'm relying on some random burst of inspiration to get to the solution.

Posted by fwaff on 2003-03-14 00:27:57