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A325820 Multiplication table for carryless product i X j in base 3 for i >= 0 and j >= 0, read by antidiagonals. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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

EXAMPLE

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.

PROG

(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];

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. also A004247, A048720.

Sequence in context: A145264 A300333 A323473 * A109042 A322403 A128540

Adjacent sequences:  A325817 A325818 A325819 * A325821 A325822 A325823

KEYWORD

nonn,base,tabl

AUTHOR

Antti Karttunen, May 22 2019

STATUS

approved

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Last modified September 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)