Re: [math-fun] Square (& other) chains and necklaces.

Thanks again. In all these cases the valences increase steadily. Not enough to employ Dirac's Theorem, but to make `for all sufficiently large n' plausible for functions which are not increasing too rapidly. The Fibonacci numbers (and presusumably other recurring sequences) seem to be the interesting cut-off point. Elwyn Berlekamp and I have shown that there are `Fibonacci chains' (no necklaces) just for n = 9, 11 and F_k - 1 and F_k for k > 3. R.