A325821 Multiplication table for carryless product i X j in base 3 for i >= 1 and j >= 1, read by antidiagonals.

1, 2, 2, 3, 1, 3, 4, 6, 6, 4, 5, 8, 9, 8, 5, 6, 7, 12, 12, 7, 6, 7, 3, 15, 16, 15, 3, 7, 8, 5, 18, 11, 11, 18, 5, 8, 9, 4, 21, 24, 13, 24, 21, 4, 9, 10, 18, 24, 19, 21, 21, 19, 24, 18, 10, 11, 20, 27, 23, 26, 9, 26, 23, 27, 20, 11, 12, 19, 30, 36, 19, 15, 15, 19, 36, 30, 19, 12, 13, 24, 33, 40, 45, 12, 13, 12, 45, 40, 33, 24, 13, 14, 26, 36, 44, 50, 54, 11, 11, 54, 50, 44, 36, 26, 14

Offset: 1

Author

Antti Karttunen, May 22 2019

Keywords

• nonn
• base
• tabl

Comments

This is table A325820 without the zero row and column. See there for more comments.

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5050; the first 100 antidiagonals of array
• Index entries for sequences related to carryless arithmetic

Crossrefs

Cf. A003991, A091257, A325820.

Programs

PARI

up_to = 105;
A325820sq(b, c) = fromdigits(Vec(Pol(digits(b,3))*Pol(digits(c,3)))%3, 3);
A325821list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A325820sq(col,(a-(col-1))))); (v); };
v325821 = A325821list(up_to);
A325821(n) = v325821[n];