Divergent RATS sequences (Q2719870)

In a RATS sequence, \(a_{i+1}\) is obtained from \(a_i\) by adding \(a_i\) to its reversal, discarding zeros, and arranging the digits in non-decreasing order. Denoting a group of \(n\) digits \(m\) by \(m^n\), it is found that in base 10 if \(a_i= 5^2 6^m 7^4\) \((m\geq 2)\) then \(a_{i+2}= 5^2 6^{m+1} 7^4\). Hence the sequence diverges and is said to have length 2 since \(i\) increases by 2. NEWLINENEWLINENEWLINEThe present paper gives, without proofs, a number of divergent RATS sequences in various bases and of various lengths. If \(t\) is a prime or pseudoprime then a RATS sequence of length \(t\) is constructed in base \((2^t-1)^2+1\). NEWLINENEWLINENEWLINESome questions and conjectures are given.