A059692 Table of carryless products i * j, i>=0, j>=0, read by antidiagonals.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 4, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 9, 8, 5, 0, 0, 6, 0, 2, 2, 0, 6, 0, 0, 7, 2, 5, 6, 5, 2, 7, 0, 0, 8, 4, 8, 0, 0, 8, 4, 8, 0, 0, 9, 6, 1, 4, 5, 4, 1, 6, 9, 0, 0, 10, 8, 4, 8, 0, 0, 8, 4, 8, 10, 0, 0, 11, 20, 7, 2, 5, 6, 5, 2, 7, 20, 11, 0

Offset: 0

Author

Henry Bottomley, Feb 19 2001

Keywords

• nonn
• base
• easy
• tabl
• look

Examples

			Table begins:
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0 ...
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ...
  0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 20 ...
  0, 3, 6, 9, 2, 5, 8, 1, 4, 7, 30, 33, 36, 39, 32, 35 ...
  0, 4, 8, 2, 6, 0, 4, 8, 2, 6, 40, 44, 48, 42, 46, 40 ...
  ...
T(12, 97) = 954 since we have 12 X 97 = carryless sum of 900, (180 mod 100=)80, 70 and (14 mod 10=)4 = 954.
		

Links

• Stefano Spezia, First 140 antidiagonals of the table, 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

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

Cf. A048720 (binary), A325820 (ternary).

Programs

Mathematica

len[num_]:=Length[IntegerDigits[num]]; digit[num_,d_]:=Part[IntegerDigits[num],d]; T[i_, j_] := FromDigits[Reverse[CoefficientList[PolynomialMod[Sum[digit[i,c]*x^(len[i]-c), {c, len[i]}]*Sum[digit[j,r]*x^(len[j]-r), {r, len[j]}], 10], x]]]; Flatten[Table[T[i - j, j], {i, 0, 12}, {j, 0, i}]] (* Stefano Spezia, Sep 26 2022 *)

PARI

T(n,k) = fromdigits(lift(Vec( Mod(Pol(digits(n)),10) * Pol(digits(k))))); \\ Kevin Ryde, Sep 27 2022

Extensions

Minor edits by N. J. A. Sloane, Aug 24 2010