A359697 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) is carryless product n X k base 10.

1, 2, 4, 3, 6, 9, 4, 8, 2, 6, 5, 0, 5, 0, 5, 6, 2, 8, 4, 0, 6, 7, 4, 1, 8, 5, 2, 9, 8, 6, 4, 2, 0, 8, 6, 4, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 12, 24, 36, 48, 50, 62, 74, 86, 98, 120, 132, 144

Offset: 1

Author

Seiichi Manyama, Mar 08 2023

Keywords

• nonn
• tabl
• base
• look

Examples

			Triangle begins:
   1;
   2,  4;
   3,  6,  9;
   4,  8,  2,  6;
   5,  0,  5,  0,  5;
   6,  2,  8,  4,  0,  6;
   7,  4,  1,  8,  5,  2,  9;
   8,  6,  4,  2,  0,  8,  6,  4;
   9,  8,  7,  6,  5,  4,  3,  2,  1;
  10, 20, 30, 40, 50, 60, 70, 80, 90, 100;
  11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121;
  12, 24, 36, 48, 50, 62, 74, 86, 98, 120, 132, 144;
		

Links

• Seiichi Manyama, Rows n = 1..99, flattened
• David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
• Index entries for sequences related to carryless arithmetic

Crossrefs

T(n,n) gives A059729.

Cf. A001477 for carryless 1 X n, A004520 for carryless 2 X n base 10, A055120 for carryless 9 X n, A008592 for carryless 10 X n, A059691 for carryless 12 X n.

Programs

PARI

T(n, k) = fromdigits(Vec(Pol(digits(n))*Pol(digits(k)))%10);