Recently (2016) Cilleruelo, Luca and Baxter proved that 10 is not unique in having the property that every number is the sum of 3 palindromes in that base. A261132and since this is always possible, we know that all entries in this sequence are at least 1. How many can you think of? Show someĮvery integer is a sum of at most 3 palindromes in base 10. It is perhaps surprising at first to learn that all numbers are palindromes in some base. On this page we will not count such numbers as palindromes. We usually don't write initial 0s in a number but if we did then 10 would also be a palindrome since it is 010. Whether a number is a palindrome or not depends on which base it is represented in but all numbersare palindromic in some base.Īll numbers are palindromes in some baseFor example 21 is not a palindromein base 10, but it is in base 2: 21 = 10101 2. We can have palindromic numbers also for example 19291. Perhaps your name is a palindrome (BOB, ANNA, EVE)? PalindromesEvery family has a palindrome in it: MUM and DAD, since a palindrome is a word that is the same when reversed. section of questions to start your own investigations.The calculator iconindicates that there is a live interactive calculator in that section. Contents of this page The icon means there is a You Do the Maths.

6 base palindromic sequence