A108760 Irregular array: n-th row consists of nonnegative integers i less than n such that n divides i(i+1).

0, 1, 0, 2, 0, 3, 0, 4, 0, 2, 3, 5, 0, 6, 0, 7, 0, 8, 0, 4, 5, 9, 0, 10, 0, 3, 8, 11, 0, 12, 0, 6, 7, 13, 0, 5, 9, 14, 0, 15, 0, 16, 0, 8, 9, 17, 0, 18, 0, 4, 15, 19, 0, 6, 14, 20, 0, 10, 11, 21, 0, 22, 0, 8, 15, 23, 0, 24, 0, 12, 13, 25, 0, 26, 0, 7, 20, 27, 0, 28, 0, 5, 9, 14, 15, 20, 24, 29

Offset: 2

Author

Robert Phillips (bobp(AT)usca.edu), Jun 24 2005

Keywords

• nonn
• easy
• tabf

Comments

Row n starts with 0 and ends with n-1.

Row n of this irregular array can be viewed as the first row of an infinite matrix with elements a_{j,i} = T(n,i)+n*j. That matrix consists of all nonnegative integers i such that n divides i(i+1).

I use these matrices to generate subsequences of A012132, as you may see on page 9 of my referenced work.

Examples

			Row 12 is 0,3,8,11 which is the first row of the matrix:
   0  3  8 11
  12 15 20 23
  24 27 32 35
  ...
giving all nonnegative integers i such that 12 divides i(i+1) (cf. A108752).
Array begins:
  0, 1;
  0, 2;
  0, 3;
  0, 4;
  0, 2, 3, 5;
  0, 6;
  0, 7;
  0, 8;
  0, 4, 5, 9;
  ...
		

Links

• Robert Phillips, Triangular Numbers which are sums of two Triangular Numbers

Crossrefs

Cf. A012132, A108752.

Programs

Python

[i for n in range(2, 30) for i in range(0, n) if i*(i+1)%n==0] # Andrey Zabolotskiy, Mar 19 2022

Extensions

Edited by Andrey Zabolotskiy, Mar 19 2022