A349520 -id:A349520 - cp's OEIS frontend

A084855 Triangular array, read by rows: T(n,k) = concatenated decimal representations of k and n, 1<=k<=n.

11, 12, 22, 13, 23, 33, 14, 24, 34, 44, 15, 25, 35, 45, 55, 16, 26, 36, 46, 56, 66, 17, 27, 37, 47, 57, 67, 77, 18, 28, 38, 48, 58, 68, 78, 88, 19, 29, 39, 49, 59, 69, 79, 89, 99, 110, 210, 310, 410, 510, 610, 710, 810, 910, 1010, 111, 211, 311, 411, 511, 611, 711, 811, 911, 1011, 1111

Offset: 1

Reinhard Zumkeller, Jun 09 2003

Indranil Ghosh, Rows 1..100 of triangle, flattened

Cf. A020338, A055642, A066686, A067574, A084854, A349520.

def T(n, k): return int(str(k) + str(n))
def auptorow(maxrow):
    return [T(n, k) for n in range(1, maxrow+1) for k in range(1, n+1)]
print(auptorow(11)) # Michael S. Branicky, Nov 21 2021

T(n, k) = k*10^A055642(n) + n.

T(n, n) = A020338(n).

A349526 Modified lexicographic ordering of all pairs i,j with 1 <= i <= j; every pair i,j of positive integers occurs exactly once.

Original entry on oeis.org

1, 1, 2, 2, 1, 3, 2, 3, 3, 1, 4, 2, 4, 3, 4, 4, 1, 5, 2, 5, 3, 5, 4, 5, 5, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6, 6, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 7, 7, 1, 8, 2, 8, 3, 8, 4, 8, 5, 8, 6, 8, 7, 8, 8, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9, 8, 9, 9, 1, 10, 2, 10, 3

Offset: 1

Clark Kimberling, Nov 21 2021

nonn

Concatenate segments: 1 1, then 1 2 2 2, then 1 3 2 3 3 3, etc., 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.  So far, the procedure leaves A349520.  Now, for each number that occurs three times in succession, remove the third occurrence, leaving the present sequence, which has the property that every pair i,j of positive integers occurs exactly once.
The pair n,1 occurs as a(n^2), a(n^2+1).
Is this a duplicate of A329949? - R. J. Mathar, Jan 06 2022

Cf. A097283, A097285, A339399, A349520, A349946, A349947, A329949.

t = {1, 1}; Do[t = Join[t, Riffle[Range[n], n], {n}], {n, 2, 10}];
u = Flatten[Partition[t, 2]];
v = Table[n (n + 1), {n, 1, 10}];
Delete[u, Map[{#} &, v]]

def auptoj(maxj):
    alst = []
    for j in range(1, maxj+1):
        for i in range(1, j+1):
            if i != j: alst.extend([i, j])
            else: alst.append(i)
    return alst
print(auptoj(10)) # Michael S. Branicky, Nov 21 2021

cp's OEIS Frontend

A084855 Triangular array, read by rows: T(n,k) = concatenated decimal representations of k and n, 1<=k<=n.

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