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, ...

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, 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, 7, 8, 8, 8, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9

Offset: 1

Author

Clark Kimberling, Nov 20 2021

Keywords

• nonn

Comments

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.

Links

• David A. Corneth, Table of n, a(n) for n = 1..10100

Crossrefs

Cf. A084855, A097283, A097285, A339399.

Programs

Mathematica

t = {1, 1}; Do[t = Join[t, Riffle[Range[n], n], {n}], {n, 2, 10}];
Flatten[Partition[t, 2]]

Python

def auptoj(maxj):
    alst = []
    for j in range(1, maxj+1):
        for i in range(1, j+1):
            alst.extend([i, j])
    return alst
print(auptoj(9)) # Michael S. Branicky, Nov 21 2021