A325821 - OEIS

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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

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OFFSET

1,2

COMMENTS

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

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

EXAMPLE

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, ...

PROG

(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];

CROSSREFS

Cf. A003991, A091257, A325820.

Sequence in context: A089913 A257522 A059897 * A341607 A303719 A299595

Adjacent sequences: A325818 A325819 A325820 * A325822 A325823 A325824

KEYWORD

nonn,base,tabl

AUTHOR

Antti Karttunen, May 22 2019

STATUS

approved