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

1,8

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.

Links

Table of n, a(n) for n=1..86.

Wikipedia, Sierpiński carpet

Example

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),
    ...

Prog

(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]))

Crossrefs

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

Sequence in context: A300333 A357019 A352562 * A352909 A323473 A341288

Adjacent sequences: A362323 A362324 A362325 * A362327 A362328 A362329

Keyword

nonn,tabf,base

Author

Rémy Sigrist, Apr 16 2023

Status

approved