A positive integer n is called a palindrome if the decimal representation of n reads the same backward as forward. Domotorp asked and Tao answered that the sequence of palindromes does not contain arbitrarily long arithmetic progressions. From Tao's comments, it is expected that the length of such the progressions should be less than 10⁸. However, his method only leads to an upper bound such as 10⁸ and does not give the exact value of the length. In this article, we determine the length of longest arithmetic progressions of palindromes.

中文翻译：

---

回文最长的算术级数

一个正整数Ñ如果的十进制表示被称为回文Ñ读取相同的向后向前。Domotorp问道，Tao回答说，回文序列不包含任意长的算术级数。从陶的评论中，可以预期，这种进展的长度应小于10 ⁸。但是，他的方法仅导致一个上限，例如10 ^8，而没有给出长度的确切值。在本文中，我们确定回文最长的算术级数的长度。