A049769 Triangular array T read by rows: T(n,k) = (k^3 mod n) + (n^3 mod k).

0, 1, 0, 1, 3, 0, 1, 0, 4, 0, 1, 4, 4, 5, 0, 1, 2, 3, 4, 6, 0, 1, 2, 7, 4, 9, 7, 0, 1, 0, 5, 0, 7, 2, 8, 0, 1, 9, 0, 2, 12, 3, 2, 9, 0, 1, 8, 8, 4, 5, 10, 9, 2, 10, 0, 1, 9, 7, 12, 5, 12, 3, 9, 11, 11, 0, 1, 8, 3, 4, 8, 0, 13, 8, 9, 12, 12, 0

Offset

1,5

Links

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

Formula

T(n, k) = A048154(n, k) + A049761(n, k). - Michel Marcus, Dec 13 2019

Example

Triangle begins as:
  0;
  1, 0;
  1, 3, 0;
  1, 0, 4, 0;
  1, 4, 4, 5, 0;
  1, 2, 3, 4, 6, 0;
  1, 2, 7, 4, 9, 7, 0;
  1, 0, 5, 0, 7, 2, 8, 0;

Maple

seq(seq( `mod`(k^3, n) + `mod`(n^3, k), k = 1..n), n = 1..15); # G. C. Greubel, Dec 13 2019

Mathematica

Table[PowerMod[k, 3, n] + PowerMod[n, 3, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Dec 13 2019 *)

Prog

(PARI) T(n, k) = lift(Mod(k, n)^3) + lift(Mod(n, k)^3);
for(n=1, 15, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Dec 13 2019
(Magma) [[Modexp(k, 3, n) + Modexp(n, 3, k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019
(Sage) [[power_mod(k, 3, n) + power_mod(n, 3, 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, 3, n) + PowerMod(n, 3, k) ))); # G. C. Greubel, Dec 13 2019

Crossrefs

Cf. A048154, A049761, A049767.

Sequence in context: A108197 A318455 A363029 * A117179 A111526 A117178

Adjacent sequences: A049766 A049767 A049768 * A049770 A049771 A049772

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved