A362329 - OEIS

%I #4 Apr 20 2023 09:00:03

%S 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,

%T 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,

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

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

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

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

%C See A362326 for the other pairs.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_carpet">Sierpiński carpet</a>

%e The first pairs are:

%e     (1, 1),

%e     (1, 4), (4, 1),

%e     (3, 3),

%e     (3, 4), (4, 3),

%e     (1, 7), (3, 5), (4, 4), (5, 3), (7, 1),

%e     (4, 5), (5, 4),

%e     (5, 5),

%e     (1, 10), (4, 7), (7, 4), (10, 1),

%e     ...

%o (PARI) is(i, j) = { while (i && j, if (i%3==1 && j%3==1, return (0), i\=3; j\=3;);); return (1); }

%o row(ij) = apply (i -> [i, ij-i], select(i -> !is(i, ij-i), [0..ij]))

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

%K nonn,tabf,base

%O 1,4

%A _Rémy Sigrist_, Apr 16 2023