A049759 Triangular array T read by rows: T(n,k)=n^2 mod k, for k=1,2,...,n, n=1,2,...

0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 4, 1, 0, 0, 0, 1, 0, 4, 4, 1, 0, 0, 1, 0, 1, 1, 3, 4, 1, 0, 0, 0, 1, 0, 0, 4, 2, 4, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 4, 1, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 1, 0, 0, 1, 1, 1, 4, 1, 1, 1, 7, 9, 4, 1, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  0;
  0, 0;
  0, 1, 0;
  0, 0, 1, 0;
  0, 1, 1, 1, 0;
  0, 0, 0, 0, 1, 0;
  0, 1, 1, 1, 4, 1, 0;
  0, 0, 1, 0, 4, 4, 1, 0;
  0, 1, 0, 1, 1, 3, 4, 1, 0;
  0, 0, 1, 0, 0, 4, 2, 4, 1, 0;
  0, 1, 1, 1, 1, 1, 2, 1, 4, 1, 0;
  0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 1, 0;
  0, 1, 1, 1, 4, 1, 1, 1, 7, 9, 4, 1, 0;
		

Links

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

Crossrefs

Cf. A048152.

Programs

GAP

Flat(List([1..15], n-> List([1..n], k-> PowerMod(n,2,k) ))); # G. C. Greubel, Dec 13 2019

Magma

[[Modexp(n,2,k): k in [1..n]]: n in [1..15]]; // G. C. Greubel, Dec 13 2019

Maple

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

Mathematica

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

PARI

tabl(nn) = {for (n=1, nn, for (k=1, n, print1(n^2 % k, ", ");); print(););} \\ Michel Marcus, Mar 31 2014

Sage

[[power_mod(n,2,k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 13 2019