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 A059692 Table of carryless products i * j, i>=0, j>=0, read by antidiagonals. 4
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 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. EXAMPLE 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. 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 *) PROG (PARI) T(n, k) = fromdigits(lift(Vec( Mod(Pol(digits(n)), 10) * Pol(digits(k))))); \\ Kevin Ryde, Sep 27 2022 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). Sequence in context: A057893 A048720 A067138 * A353109 A336225 A004247 Adjacent sequences: A059689 A059690 A059691 * A059693 A059694 A059695 KEYWORD nonn,base,easy,tabl,look AUTHOR Henry Bottomley, Feb 19 2001 EXTENSIONS Minor edits by N. J. A. Sloane, Aug 24 2010 STATUS approved

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Last modified March 25 18:33 EDT 2023. Contains 361528 sequences. (Running on oeis4.)