Recall Sloane's old request for more terms of A003459 2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 199 311 337 373 733 919 991 and Rich's astonishing observation that the next term is 1111111111111111111. Absent Rich's analysis, trying to extend this sequence makes a great set of beginner's programming exercises. Of course, we can't expect to reach (10^19-1)/9, but we can at least see how far we can push the bound. As I explained to a 7th grader, even restricting the search to combinations of the four digits 1,3,7,9 entails numbers like 4^18 ~ 10^11. But the 7th grader is at this very moment having heart surgery, and to keep occupied, I added some speedups to our search program: only look at starting numbers with nondecreasing digits, and generate only unique digit combinations, and only as needed. (We get the target sequence afterward by generating and merging the various permutations, and fudging the initial 2,3,5,7.) To my amazement the (uncompiled, Macsyma) program printed 11,13,...,199,337, and after about a minute, 1111111111111111111 ! And after a few more minutes, (10^23-1)/9 ! Here's hoping the 7th grader wakes up with enough neurons to appreciate why these speedups are way bigger than they initially seem. PS, I seem to have lost the mail with Rich's proof. Where are the old archives?.