A084855 -id:A084855 - cp's OEIS frontend

A084854 Triangular array, read by rows: T(n,k) = concatenated decimal representations of n and k, 1<=k<=n.

11, 21, 22, 31, 32, 33, 41, 42, 43, 44, 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 66, 71, 72, 73, 74, 75, 76, 77, 81, 82, 83, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 1010, 111, 112, 113, 114, 115, 116, 117, 118, 119, 1110, 1111

Offset: 1

Reinhard Zumkeller, Jun 09 2003

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

Cf. A017281, A020338, A055642, A066686, A067574, A084855.

def T(n, k): return int(str(n) + str(k))
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) = n*10^A055642(k) + k.

T(n, 1) = A017281(n); T(n, n) = A020338(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, ...

Original entry on oeis.org

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

Clark Kimberling, Nov 20 2021

nonn

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.

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

Cf. A084855, A097283, A097285, A339399.

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

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

cp's OEIS Frontend

A084854 Triangular array, read by rows: T(n,k) = concatenated decimal representations of n and k, 1<=k<=n.

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