An emirp is a prime number with the property that if we write down the digits in base $10$ in reverse , we again get a prime number. Trivial emirp's are the palindrome primes (if we write down the digits in reverse , we get the same prime number).
What about Carmichael numbers with the property that writing down them in reverse (of course again in base $10$) leads to another Carmichael number ?
The Carmichael number $101101$ is a trivial case (palindrome). It is so far the only Carmichael number I found with this property. I have not checked the database upto $10^{21}$ yet.
$15709$ is the smallest example , if we only demand the number to be composite and to pass the weak fermat test with base $2$ , but neither of the numbers are Carmichael numbers.
I am curious whether there is a nontrivial case. or at least further palindromes.