A049767 Triangular array T, read by rows: T(n,k) = (k^2 mod n) + (n^2 mod k), for k = 1..n and n >= 1.

0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 5, 5, 2, 0, 1, 4, 3, 4, 2, 0, 1, 5, 3, 3, 8, 2, 0, 1, 4, 2, 0, 5, 8, 2, 0, 1, 5, 0, 8, 8, 3, 8, 2, 0, 1, 4, 10, 6, 5, 10, 11, 8, 2, 0, 1, 5, 10, 6, 4, 4, 7, 10, 8, 2, 0, 1, 4, 9, 4, 5, 0, 5, 4, 9, 8, 2, 0, 1, 5, 10, 4

Offset

1,5

Links

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Formula

T(n, k) = A048152(n, k) + A049759(n, k). - Michel Marcus, Nov 21 2019

Example

Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  0;
  1,  0;
  1,  2,  0;
  1,  0,  2,  0;
  1,  5,  5,  2,  0;
  1,  4,  3,  4,  2,  0;
  1,  5,  3,  3,  8,  2,  0;
  1,  4,  2,  0,  5,  8,  2,  0;
  1,  5,  0,  8,  8,  3,  8,  2,  0;
  1,  4, 10,  6,  5, 10, 11,  8,  2,  0;
  ...

Maple

seq(seq( `mod`(k^2, n) + `mod`(n^2, k), k = 1..n), n = 1..15); # G. C. Greubel, Dec 13 2019

Mathematica

Table[PowerMod[k, 2, n] + PowerMod[n, 2, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Dec 13 2019 *)

Prog

(PARI) T(n, k) = lift(Mod(k, n)^2) + lift(Mod(n, k)^2);
for(n=1, 15, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Dec 13 2019
(Magma) [[Modexp(k, 2, n) + Modexp(n, 2, k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019
(Sage) [[power_mod(k, 2, n) + power_mod(n, 2, k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019
(GAP) Flat(List([1..15], n-> List([1..n], k-> PowerMod(k, 2, n) + PowerMod(n, 2, k) ))); # G. C. Greubel, Dec 13 2019

Crossrefs

Row sums are in A049768.

Cf. A048152, A049759.

Sequence in context: A158944 A156663 A139366 * A286351 A091394 A029881

Adjacent sequences: A049764 A049765 A049766 * A049768 A049769 A049770

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved