Palindromic number

A nonnegative integer whose positional notation reads the same forwards and backwards, with no leading zeros. This property depends on the base: $585$ is a palindromic number in both decimal representation and binary representation, since $585=(1001001001{)}_2$.

A palindromic number in binary representation, with no leading zeros. Every positive binary palindrome is an odd number, because its first and last numerical digits must both be one.

A palindromic number in decimal representation, with no leading zeros.

A positive integer whose repeated reverse-and-add process never reaches a palindromic number in the chosen base. Each step adds the current number to the number obtained by reversing its numerical digits. Failure to find a palindromic number after a fixed iteration limit establishes only a candidate, not a proof that the process never succeeds.