Questions tagged [palindromes]

$2017:$ Was initially asked on MSE - but wasn't solved or updated there since. Update $2019$: I've returned to this problem, made some progress and updated the post here. (I've basically rewritten ...

This question was already asked earlier at MSE. Let $M$ denote the sequence of values of $\mu(n)$, the Möbius function which begins $M = (1,-1,-1,0,-1,1,-1,0,\dotsc)$. The questions below concern ...

Helfgott proved that any odd number greater than 5 is the sum of three primes. Cilleruelo and Luca proved that every positive integer is the sum of three palindromes. Is every integer greater than 1 ...

Question: Does there exist $a,n \in \mathbb{Z}^+$, where $n \geq 2$, such that $$a, an, an^2,an^3,\ldots,an^5$$ are all palindromes in base 10? We see that $a=1$ and $n=11$ give rise to $$1, 11, 121, ...

What are the numbers that can be expressed as the sum of two palindromes? A number is a palindrome if it is the same written backwards, like 1367631. My motivation comes from the problem posed for ...