A362326 Pairs (i, j) of nonnegative integers whose ternary expansions have no common digit 1 sorted first by i + j then by i.

0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 3, 1, 2, 2, 1, 3, 0, 0, 4, 1, 3, 2, 2, 3, 1, 4, 0, 0, 5, 2, 3, 3, 2, 5, 0, 0, 6, 1, 5, 2, 4, 4, 2, 5, 1, 6, 0, 0, 7, 1, 6, 2, 5, 5, 2, 6, 1, 7, 0, 0, 8, 2, 6, 6, 2, 8, 0, 0, 9, 1, 8, 2, 7, 3, 6, 6, 3, 7, 2, 8, 1, 9, 0, 0, 10

Offset: 1

Author

Rémy Sigrist, Apr 16 2023

Keywords

• nonn
• tabf
• base

Comments

This sequence is to Sierpinski carpet what A352909 is to Sierpinski gasket.

There are A293974(n + 1) pairs (i, j) with n = i + j.

See A362329 for the other pairs.

Examples

			The first pairs are:
    (0, 0),
    (0, 1), (1, 0),
    (0, 2), (2, 0),
    (0, 3), (1, 2), (2, 1), (3, 0),
    (0, 4), (1, 3), (2, 2), (3, 1), (4, 0),
    (0, 5), (2, 3), (3, 2), (5, 0),
    (0, 6), (1, 5), (2, 4), (4, 2), (5, 1), (6, 0),
    (0, 7), (1, 6), (2, 5), (5, 2), (6, 1), (7, 0),
    (0, 8), (2, 6), (6, 2), (8, 0),
    ...
		

Links

• Wikipedia, Sierpiński carpet

Crossrefs

Cf. A293974, A352909, A362327 (i-values), A362328 (j-values), A362329 (complement).

Programs

PARI

is(i, j) = { while (i && j, if (i%3==1 && j%3==1, return (0), i\=3; j\=3;);); return (1); }
row(ij) = apply (i -> [i, ij-i], select(i -> is(i, ij-i), [0..ij]))