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A349520 Let S_k denote the list of pairs (1,k), (2,k), (3,k), ..., (k,k); sequence lists the pairs in S_1, S_2, S_3, ...

%I A349520 #12 Nov 21 2021 23:29:44
%S A349520 1,1,1,2,2,2,1,3,2,3,3,3,1,4,2,4,3,4,4,4,1,5,2,5,3,5,4,5,5,5,1,6,2,6,
%T A349520 3,6,4,6,5,6,6,6,1,7,2,7,3,7,4,7,5,7,6,7,7,7,1,8,2,8,3,8,4,8,5,8,6,8,
%U A349520 7,8,8,8,1,9,2,9,3,9,4,9,5,9,6,9,7,9
%N A349520 Let S_k denote the list of pairs (1,k), (2,k), (3,k), ..., (k,k); sequence lists the pairs in S_1, S_2, S_3, ...
%C A349520 Concatenate segments: 1 1, then 1 2 2 2, then 1 3 2 3 3 3, so that the general segment is 1 n 2 n ... n n.  This is followed by 1; thus, not only does every i,j with i <= j occur, but so does every i,j with i >= j. Every pair i,j of positive integers with i < j or i > j occurs exactly once.
%H A349520 David A. Corneth, <a href="/A349520/b349520.txt">Table of n, a(n) for n = 1..10100</a>
%t A349520 t = {1, 1}; Do[t = Join[t, Riffle[Range[n], n], {n}], {n, 2, 10}];
%t A349520 Flatten[Partition[t, 2]]
%o A349520 (Python)
%o A349520 def auptoj(maxj):
%o A349520     alst = []
%o A349520     for j in range(1, maxj+1):
%o A349520         for i in range(1, j+1):
%o A349520             alst.extend([i, j])
%o A349520     return alst
%o A349520 print(auptoj(9)) # _Michael S. Branicky_, Nov 21 2021
%Y A349520 Cf. A084855, A097283, A097285, A339399.
%K A349520 nonn
%O A349520 1,4
%A A349520 _Clark Kimberling_, Nov 20 2021