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A362329
Pairs (i, j) of nonnegative integers whose ternary expansions have a common digit 1 sorted first by i + j then by i.
3
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.
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
KEYWORD
nonn,tabf,base
AUTHOR
Rémy Sigrist, Apr 16 2023
STATUS
approved