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An algebraic question I have been working on led me to a sequence that appears in OEIS as A186355: "adjusted joint rank sequence of $(f(i))$ and $(g(j))$ with $f(i)$ before $g(j)$ when $f(i)=g(j)$, where $f(i)=3i$ and $g(j)=j(j+1)/2$". This means that we assign to elements of these sequences positive integers such that every integer appears exactly once by assigning to each element the order in which it appears if we merge the two sequences, keeping pairs of equal elements in order ($f$ before $g$).

The OEIS entry does not really say how constructions like that appear. Can anyone enlighten me if there are some conceptual things behind such a construction?

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  • $\begingroup$ OEIS A186355 has a link to a duplicate sequence A089108 which has a paper cited which gives additional information and further references. $\endgroup$
    – Nemo
    Commented Mar 2 at 19:15
  • $\begingroup$ @CaveJohnson thanks! In principle it is not clear that the two sequences coincide (with each other or with the sequence I am thinking of). But it is an interesting angle. Alas that paper has nothing on joint rank, which is what my question is about. $\endgroup$
    – Vladimir Dotsenko
    Commented Mar 2 at 19:36

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