Re: [math-fun] Digital silliness

For a number n, let f(n) be the set of numbers gotten by splitting n^2 at the 0 digits. For example

29648^2 = 879003904

so f(29648) = { 4, 39, 879 }

Let S be the smallest set of numbers containing 2 and fixed by f. What is the largest element of S?

perhaps you mean "if s in S , then f(s) is a subset of S ". it is not obvious to me that S is finite. it is easy to exhibit arbitrarily large integers that do not have 0 as a decimal digit, and whose squares also do not have any 0's . of course this does not show that your S is infinite, but raises that issue as a possibility. is there reason to believe (i.e. an heuristic argument) that S is finite? or better yet, a proof? mike