Kerry wrote:
There's a 540-word variation on the "A man, a plan, a canal--Panama." palindrome here:
http://www.jy-muggeridge.freeserve.co.uk/pals_hoey.htm
Kerry -- lkmitch@att.net www.fractalus.com/kerry
As long as we're on the subject, here's a .sig I posted (thru Rich) about a year and a half ago: FromCharacterCode[Mod[113-ContinuedFraction[ Sqrt[94526554335373222890113921736835432]][[2]],116]] You may need a recent version of Mma to get it to execute; it's not hard to do something similar in base 36. David Terr asked back then:
Cute! Can all palindromes be constructed this way? David
I responded: "Not directly. You have to look at the parity class. If you look at the convergents P_i/Q_i of the continued fraction mod 2, then P_{n-1}*Q_{n-1} has to be even, where n is the length of the palindrome. For even-length palindromes, the number of possible parity classes is N(2m)=((-1)^m + 2^(m+1))/3. For odd-length palindromes, it's N(2m+1)=((-1)^m + 5 2^m)/3. In this case, the parity class of the original was prohibited, but the parity class of the complement was not. That's why the subtraction is in there. I'm pretty sure that you could do similar things for any palindrome to coax the numbers into a valid parity class if they're not immediately cooperative." For more details, see J. Mc Laughlin, "Multi-variable polynomial solutions to Pell's equation and fundamental units in real quadratic fields" www.math.uiuc.edu/~jgmclaug/polypel2c.ps or www.math.uiuc.edu/~jgmclaug/polypel2c.pdf -- Mike Stay staym@clear.net.nz http://www.xaim.com/staym