A362331 -id:A362331 - cp's OEIS frontend

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

Rémy Sigrist, Apr 16 2023

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.

			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),
    ...

Wikipedia, Sierpiński carpet

Cf. A293974, A353296, A362326 (complement), A362330 (i-values), A362331 (j-values).

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]))

A362330 The i-values of pairs (i, j) listed in A362329.

Original entry on oeis.org

1, 1, 4, 3, 3, 4, 1, 3, 4, 5, 7, 4, 5, 5, 1, 4, 7, 10, 1, 4, 7, 10, 13, 3, 12, 3, 4, 12, 13, 1, 3, 4, 5, 7, 10, 12, 13, 14, 16, 4, 5, 9, 13, 14, 5, 9, 10, 14, 1, 4, 7, 9, 10, 11, 13, 16, 19, 9, 10, 11, 12, 9, 10, 11, 12, 13, 1, 4, 7, 9, 10, 11, 12, 13, 14, 16

Offset: 1

Rémy Sigrist, Apr 16 2023

See A362331 for the j-values.

Rémy Sigrist, Table of n, a(n) for n = 1..13426

Cf. A362329, A362331 (j-values).

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

cp's OEIS Frontend

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

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