A048152 Triangular array T read by rows: T(n,k) = k^2 mod n, for 1 <= k <= n, n >= 1.

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, 0

Offset

1,12

Links

T. D. Noe, Rows n = 1..100 of triangle, flattened

Eric Weisstein's World of Mathematics, Quadratic Residue

Formula

T(n,k) = A133819(n,k) mod n, k = 1..n. - Reinhard Zumkeller, Apr 29 2013

T(n,k) = (T(n,k-1) + (2k+1)) mod n. - Andrés Ventas, Apr 06 2021

Example

Rows:
  0;
  1, 0;
  1, 1, 0;
  1, 0, 1, 0;
  1, 4, 4, 1, 0;
  1, 4, 3, 4, 1, 0;

Mathematica

Flatten[Table[PowerMod[k, 2, n], {n, 15}, {k, n}]] (* Harvey P. Dale, Jun 20 2011 *)

Prog

(Haskell)
a048152 n k = a048152_tabl !! (n-1) !! (k-1)
a048152_row n = a048152_tabl !! (n-1)
a048152_tabl = zipWith (map . flip mod) [1..] a133819_tabl
-- Reinhard Zumkeller, Apr 29 2013

Crossrefs

Cf. A060036.

Cf. A225126 (central terms).

Cf. A070430 (row 5), A070431 (row 6), A053879 (row 7), A070432 (row 8), A008959 (row 10), A070435 (row 12), A070438 (row 15), A070422 (row 20).

Cf. A046071 (in ascending order, without zeros and duplicates).

Cf. A063987 (for primes, in ascending order, without zeros and duplicates).

Sequence in context: A366464 A185057 A343720 * A350037 A070430 A336302

Adjacent sequences: A048149 A048150 A048151 * A048153 A048154 A048155

Keyword

nonn,tabl,nice,easy

Author

Clark Kimberling

Status

approved