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A343720 Triangle read by rows: T(n,k) = k^2 mod n for k = 0..n-1, n >= 1. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,13
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).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
Eric Weisstein's World of Mathematics, Quadratic Residue
FORMULA
T(n,k) = k^2 mod n.
T(n,k) = T(n,n-k).
EXAMPLE
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
PROG
(PARI) T(n, k) = k^2 % n \\ Andrew Howroyd, Jan 05 2024
CROSSREFS
Sequence in context: A366467 A366464 A185057 * A048152 A350037 A070430
KEYWORD
nonn,tabl
AUTHOR
Jon E. Schoenfield, Apr 26 2021
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)