A049765 Triangular array T, read by rows: T(n,k) = (k mod n) + (n mod k), for k = 1..n and n >= 1.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  0;
  1, 0;
  1, 3, 0;
  1, 2, 4, 0;
  1, 3, 5, 5, 0;
  1, 2, 3, 6, 6,  0;
  1, 3, 4, 7, 7,  7,  0;
  1, 2, 5, 4, 8,  8,  8,  0;
  1, 3, 3, 5, 9,  9,  9,  9,  0;
  1, 2, 4, 6, 5, 10, 10, 10, 10, 0;
  ...
		

Links

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

Crossrefs

Row sums are in A049766.

Cf. A048158, A049767, A049768.

Programs

GAP

Flat(List([1..15], n-> List([1..n], k-> (k mod n) + (n mod k) ))); # G. C. Greubel, Dec 13 2019

Magma

[[(k mod n) + (n mod k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019

Maple

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

Mathematica

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

PARI

T(n,k) = k%n + n%k;
for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 13 2019

Sage

[[(k%n) + (n%k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019