A343720 Triangle read by rows: T(n,k) = k^2 mod n for k = 0..n-1, n >= 1.

0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 4, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 2, 2, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 0, 7, 7, 0, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1

Offset: 1

Author

Jon E. Schoenfield, Apr 26 2021

Keywords

• nonn
• tabl

Comments

Similar to A048152 and A060036, but each row in this sequence begins at k = 0 and ends at k = n-1 (the minimum and maximum residues modulo n, respectively).

Examples

			Triangle begins:
  n\k| 0  1  2  3  4  5  6  7  8  9 10 11
  ---+-----------------------------------
   1 | 0
   2 | 0, 1
   3 | 0, 1, 1
   4 | 0, 1, 0, 1
   5 | 0, 1, 4, 4, 1
   6 | 0, 1, 4, 3, 4, 1
   7 | 0, 1, 4, 2, 2, 4, 1
   8 | 0, 1, 4, 1, 0, 1, 4, 1
   9 | 0, 1, 4, 0, 7, 7, 0, 4, 1
  10 | 0, 1, 4, 9, 6, 5, 6, 9, 4, 1
  11 | 0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1
  12 | 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
• Eric Weisstein's World of Mathematics, Quadratic Residue

Crossrefs

Cf. A048152, A060036.

Programs

PARI

T(n,k) = k^2 % n \\ Andrew Howroyd, Jan 05 2024

Formula

T(n,k) = k^2 mod n.

T(n,k) = T(n,n-k).