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 A186219 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186220. 35
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 OFFSET 1,2 COMMENTS Suppose that f and g are strictly increasing functions for which (f(i)) and (g(j)) are integer sequences. If 0<|d|<1, the sets F={f(i): i>=1} and G={g(j)+d: j>=1} are clearly disjoint. Let f^=(inverse of f) and g^=(inverse of g). When the numbers in F and G are jointly ranked, the rank of f(n) is a(n):=n+floor(g^(f(n))-d), and the rank of g(n)+d is b(n):=n+floor(f^(g(n))+d). Therefore, the sequences a and b are a complementary pair. Although the sequences (f(i)) and (g(j)) may not be disjoint, the sequences (f(i)) and (g(j)+d) are disjoint, and this observation enables two types of adjusted joint rankings: (1) if 0

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Last modified March 29 15:46 EDT 2023. Contains 361599 sequences. (Running on oeis4.)