A362329 Pairs (i, j) of nonnegative integers whose ternary expansions have a common digit 1 sorted first by i + j then by i.

1, 1, 1, 4, 4, 1, 3, 3, 3, 4, 4, 3, 1, 7, 3, 5, 4, 4, 5, 3, 7, 1, 4, 5, 5, 4, 5, 5, 1, 10, 4, 7, 7, 4, 10, 1, 1, 13, 4, 10, 7, 7, 10, 4, 13, 1, 3, 12, 12, 3, 3, 13, 4, 12, 12, 4, 13, 3, 1, 16, 3, 14, 4, 13, 5, 12, 7, 10, 10, 7, 12, 5, 13, 4, 14, 3, 16, 1

Offset

1,4

Comments

This sequence is to Sierpinski carpet what A353296 is to Sierpinski gasket.

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

See A362326 for the other pairs.

Links

Table of n, a(n) for n=1..78.

Wikipedia, Sierpiński carpet

Example

The first pairs are:
    (1, 1),
    (1, 4), (4, 1),
    (3, 3),
    (3, 4), (4, 3),
    (1, 7), (3, 5), (4, 4), (5, 3), (7, 1),
    (4, 5), (5, 4),
    (5, 5),
    (1, 10), (4, 7), (7, 4), (10, 1),
    ...

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, A353296, A362326 (complement), A362330 (i-values), A362331 (j-values).

Sequence in context: A053216 A325489 A278516 * A292434 A138522 A095813

Adjacent sequences: A362326 A362327 A362328 * A362330 A362331 A362332

Keyword

nonn,tabf,base

Author

Rémy Sigrist, Apr 16 2023

Status

approved