then k becomes palindromic after one iteration: k + k = 2k, which is single-digit in base b (and thus a palindrome). If k > b/2, k becomes palindromic after two iterations. The smallest number in each base which could possibly be a Lychrel number are : Extension to negative integers Lychrel numbers can be extended to the negative integers by use of a signed-digit representation to represent each integer. See also Arithmetic dynamics Palindromic number References External links John Walker – Three years of computing Tim Irvin – About two months of computing Jason Doucette – World records – 196 Palindrome Quest, Most Delayed Palindromic Number Benjamin Despres 196 and Other Lychrel Numbers by Wade VanLandingham MathPages – Digit Reversal Sums Leading to Palindromes NumberPhile All known delayed palindromic numbers – Dmitry Maslov, MDPN project Testing a delayed palindrome – Dmitry Maslov, MDPN project Arithmetic dynamics Base-dependent integer sequences Unsolved problems in number theory