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A366421 a(n) is the floor of the n-th improper fraction (including the ones of the type n/n) sorted by increasing numerator+denominator, then by numerator.

%I A366421 #25 Jan 25 2024 07:30:40
%S A366421 1,2,1,3,1,4,1,2,5,1,2,6,1,1,3,7,1,2,3,8,1,1,2,4,9,1,1,2,4,10,1,1,2,3,
%T A366421 5,11,1,1,2,3,5,12,1,1,1,2,3,6,13,1,1,2,2,4,6,14,1,1,1,2,3,4,7,15,1,1,
%U A366421 1,2,3,4,7,16,1,1,1,2,2,3,5,8,17,1,1,1,2,2,3,5,8,18
%N A366421 a(n) is the floor of the n-th improper fraction (including the ones of the type n/n) sorted by increasing numerator+denominator, then by numerator.
%F A366421 a(n) = floor[A138099(n)/(A216607(n)+1)]
%e A366421 The first such fraction is 1/1, followed by 2/1, 2/2, 3/1, 3/2 and so on, then a(1)=[1/1]=1, a(2)=[2/1]=2, a(3)=[2/2]=1, a(4)=[3/1]=3, a(5)=[3/2]=1 and so on, where [.] is the floor function.
%e A366421 Terms begin:
%e A366421   [1/1]=1,
%e A366421   [2/1]=2,
%e A366421   [2/2]=1, [3/1]=3,
%e A366421   [3/2]=1, [4/1]=4,
%e A366421   [3/3]=1, [4/2]=2, [5/1]=5,
%e A366421   [4/3]=1, [5/2]=2, [6/1]=6,
%e A366421   ...
%K A366421 nonn
%O A366421 1,2
%A A366421 _Mariano Masiello_, Nov 16 2023