A325820 Multiplication table for carryless product i X j in base 3 for i >= 0 and j >= 0, read by antidiagonals.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 1, 3, 0, 0, 4, 6, 6, 4, 0, 0, 5, 8, 9, 8, 5, 0, 0, 6, 7, 12, 12, 7, 6, 0, 0, 7, 3, 15, 16, 15, 3, 7, 0, 0, 8, 5, 18, 11, 11, 18, 5, 8, 0, 0, 9, 4, 21, 24, 13, 24, 21, 4, 9, 0, 0, 10, 18, 24, 19, 21, 21, 19, 24, 18, 10, 0, 0, 11, 20, 27, 23, 26, 9, 26, 23, 27, 20, 11, 0, 0, 12, 19, 30, 36, 19, 15, 15, 19, 36, 30, 19, 12, 0

Offset: 0

Author

Antti Karttunen, May 22 2019

Keywords

• nonn
• base
• tabl

Examples

			The array begins as:
  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, ...
  0,  2,  1,  6,  8,  7,  3,  5,  4,  18,  20,  19,  24, ...
  0,  3,  6,  9, 12, 15, 18, 21, 24,  27,  30,  33,  36, ...
  0,  4,  8, 12, 16, 11, 24, 19, 23,  36,  40,  44,  48, ...
  0,  5,  7, 15, 11, 13, 21, 26, 19,  45,  50,  52,  33, ...
  0,  6,  3, 18, 24, 21,  9, 15, 12,  54,  60,  57,  72, ...
  0,  7,  5, 21, 19, 26, 15, 13, 11,  63,  70,  68,  57, ...
  0,  8,  4, 24, 23, 19, 12, 11, 16,  72,  80,  76,  69, ...
  0,  9, 18, 27, 36, 45, 54, 63, 72,  81,  90,  99, 108, ...
  0, 10, 20, 30, 40, 50, 60, 70, 80,  90, 100,  83, 120, ...
  0, 11, 19, 33, 44, 52, 57, 68, 76,  99,  83,  91, 132, ...
  0, 12, 24, 36, 48, 33, 72, 57, 69, 108, 120, 132, 144, ...
  etc.
A(2,2) = 2*2 mod 3 = 1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
• Index entries for sequences related to carryless arithmetic

Crossrefs

Cf. A169999 (the main diagonal).

Row/Column 0: A000004, Row/Column 1: A001477, Row/Column 2: A004488, Row/Column 3: A008585, Row/Column 4: A242399, Row/Column 9: A008591.

Cf. A007089, A207669, A207670, A263273, A325825.

Cf. A325821 (same table without the zero row and column).

Cf. A048720 (binary), A059692 (decimal), A004247 (full multiply).

Programs

PARI

up_to = 105;
A325820sq(b, c) = fromdigits(Vec(Pol(digits(b,3))*Pol(digits(c,3)))%3, 3);
A325820list(up_to) = { my(v = vector(up_to), i=0); for(a=0,oo, for(col=0,a, if(i++ > up_to, return(v)); v[i] = A325820sq(a-col,col))); (v); };
v325820 = A325820list(up_to);
A325820(n) = v325820[1+n];