A343720 - OEIS

%I #9 Feb 16 2025 08:34:02

%S 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,

%T 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,

%U 4,9,4,1,0,1,4,9,4,1,0,1,4,9,3,12,10,10,12,3,9,4,1

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

%C 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).

%H Andrew Howroyd, <a href="/A343720/b343720.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuadraticResidue.html">Quadratic Residue</a>

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

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

%e Triangle begins:

%e   n\k| 0  1  2  3  4  5  6  7  8  9 10 11

%e   ---+-----------------------------------

%e    1 | 0

%e    2 | 0, 1

%e    3 | 0, 1, 1

%e    4 | 0, 1, 0, 1

%e    5 | 0, 1, 4, 4, 1

%e    6 | 0, 1, 4, 3, 4, 1

%e    7 | 0, 1, 4, 2, 2, 4, 1

%e    8 | 0, 1, 4, 1, 0, 1, 4, 1

%e    9 | 0, 1, 4, 0, 7, 7, 0, 4, 1

%e   10 | 0, 1, 4, 9, 6, 5, 6, 9, 4, 1

%e   11 | 0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1

%e   12 | 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1

%o (PARI) T(n,k) = k^2 % n \\ _Andrew Howroyd_, Jan 05 2024

%Y Cf. A048152, A060036.

%K nonn,tabl

%O 1,13

%A _Jon E. Schoenfield_, Apr 26 2021