For the time being, the OEIS website contains almost $300000$ sequences. Each of these sequences is the mark of a specific mathematical concept. Sometimes two (or more) distinct concepts have the same mark, which suggests a connection between *a priori* independent mathematical areas. The most famous example like that is perhaps the Catalan numbers sequence: A000108.

**Question**: What are the examples of pair of integer sequences coinciding on all the *known* terms, but for which the coincidence for all the terms is unknown?

Cheating is not allowed. By cheating I mean *artificial* examples like:

$u_n = v_n =n$ for $n \neq 10$, and if RH is true then $u_{10} = v_{10} = 10$, else $u_{10}+1 = v_{10} = 1$.

The existence of an OEIS entry could act as safety.

*EDIT*: I would like to point out that all the answers below are about pair of integer sequences which were already conjectured to be the same, and of course they are on-topic (and some of them are very nice). Note that such examples can be found by searching something like "conjectured to be identical" on OEIS, as I did for some of my own examples below...

Now, a more surprising kind of answer would be a (non-cheating) pair of integer sequences which are the same on the *known* entries, but for which there is no evidence *a priori* that they are the same for all the entries or that they are related (i.e. the precise meaning of a *coincidence*). Such examples, also on-topic, could reveal some unexpected connections in mathematics, but could be harder to find...