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A108760
Irregular array: n-th row consists of nonnegative integers i less than n such that n divides i(i+1).
0
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
2,4
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.
EXAMPLE
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;
...
PROG
(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
CROSSREFS
Sequence in context: A215395 A338569 A343757 * A343554 A137304 A234581
KEYWORD
nonn,easy,tabf
AUTHOR
Robert Phillips (bobp(AT)usca.edu), Jun 24 2005
EXTENSIONS
Edited by Andrey Zabolotskiy, Mar 19 2022
STATUS
approved