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A096008 Irregular triangle read by rows where n-th row contains all quadratic residues (including zero) mod n. 45
0, 0, 1, 0, 1, 0, 1, 0, 1, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 4, 0, 1, 4, 7, 0, 1, 4, 5, 6, 9, 0, 1, 3, 4, 5, 9, 0, 1, 4, 9, 0, 1, 3, 4, 9, 10, 12, 0, 1, 2, 4, 7, 8, 9, 11, 0, 1, 4, 6, 9, 10, 0, 1, 4, 9, 0, 1, 2, 4, 8, 9, 13, 15, 16, 0, 1, 4, 7, 9, 10, 13, 16, 0, 1, 4, 5, 6, 7, 9, 11, 16, 17, 0, 1, 4, 5, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,10
LINKS
Eric Weisstein's World of Mathematics, Quadratic Residue.
EXAMPLE
The table starts:
[0]
[0, 1]
[0, 1]
[0, 1]
[0, 1, 4]
[0, 1, 3, 4]
[0, 1, 2, 4]
[0, 1, 4]
[0, 1, 4, 7]
[0, 1, 4, 5, 6, 9]
...
MAPLE
q:=n-> sort(convert({seq(i^2 mod n, i=0..n-1)}, list)); # N. J. A. Sloane, Feb 09 2011
MATHEMATICA
row[n_] := Table[PowerMod[k, 2, n], {k, 0, n-1}] // Union; Table[row[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Sep 09 2013 *)
PROG
(PARI) T(n) = {local(v, r, i, j, k); v=vector(n, i, 0); for(i=0, floor(n/2), v[i^2%n+1]=1); k=sum(i=1, n, v[i]); j=0; r=vector(k); for(i=1, n, if(v[i], j++; r[j]=i-1)); r}
(Haskell)
a096008 n k = a096008_tabf !! (n-1) !! (k-1)
a096008_row n = a096008_tabf !! (n-1)
a096008_tabf = [0] : map (0 :) a046071_tabf
-- Reinhard Zumkeller, May 10 2015
CROSSREFS
Cf. A046071 (without zeros), A000224 (row lengths), A063987.
Last elements of rows give A047210.
Row sums give A165909.
Sequence in context: A298063 A298712 A127538 * A122873 A221275 A176803
KEYWORD
easy,tabf,nonn
AUTHOR
Cino Hilliard, Jul 20 2004
EXTENSIONS
Edited by Franklin T. Adams-Watters, Nov 07 2006
STATUS
approved

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Last modified March 19 07:04 EDT 2024. Contains 370953 sequences. (Running on oeis4.)