A349947 Triangular array: row n gives the positions of n+1 in A349946.

1, 2, 4, 3, 5, 9, 6, 7, 10, 16, 8, 11, 12, 17, 25, 13, 14, 18, 19, 26, 36, 15, 20, 21, 27, 28, 37, 49, 22, 23, 29, 30, 38, 39, 50, 64, 24, 31, 32, 40, 41, 51, 52, 65, 81, 33, 34, 42, 43, 53, 54, 66, 67, 82, 100, 35, 44, 45, 55, 56, 68, 69, 83, 84, 101, 121

Offset: 1

Author

Clark Kimberling, Dec 07 2021

Keywords

• nonn
• tabl

Comments

Every positive integer occurs exactly once, so as a sequence, this is a permutation of the positive integers.

Row n ends in n^2. The first term in row n is (1 + n/1)^2 - 3 if n >= 4 and n is even; as in A028872(n) for n >= 3.

The first term in row n is ((n+1)/2)^2 - 1 if n >= 3 and n is odd, as in A132411(n) for n >= 3.

Examples

			First 7 rows:
   1
   2   4
   3   5   9
   6   7  10  16
   8  11  12  17  25
  13  14  18  19  26  36
  14  20  21  27  28  37  49
		

Crossrefs

Cf. A349526, A349946.

Programs

Mathematica

t = {1, 1}; Do[t = Join[t, Riffle[Range[n], n], {n}], {n, 2, 100}];
u = Flatten[Partition[t, 2]];
v = Table[n (n + 1), {n, 1, 80}];
d = Delete[u, Map[{#} &, v]]; (* A349526 *)
p = Table[{d[[n]], d[[n + 1]]}, {n, 1, 150}];
q = Map[Total, p]  (* A349946 *)
r = Table[Flatten[Position[q, n]], {n, 2, 12}]  (* A349947 array *)
Flatten[r]  (* A349947 sequence *)