Hello Math-Fun, I've considered this lately ("Base 10 weak Skolem-Langford numbers"): https://oeis.org/A108116 The idea would be to have a "lighter constraint" on the digits. We would say: « Numbers such that for any digit "d", the _closest_ duplicate of "d" is at exactly "d" digits ». The new sequence would then admit numbers like 2002002, or 2312131 because we would drop the "unique pair (of digits)" obligation. Best, É. P.-S. My friend Carole and I are currently working on a sequence related to this post, visible here (in French), where the constraint « For any digit "d", the _closest_ duplicate of "d" is at exactly "d" digits » is applied to a sequence -- not to integers themselves: http://cinquantesignes.blogspot.com/2020/11/une-suite-facon-skolem-langford.... Yes, this is a backtracking nightmare!