|
%I #10 Apr 20 2023 03:52:40
%S 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,
%T 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,
%U 0,9,1,8,2,7,3,6,6,3,7,2,8,1,9,0,0,10
%N Pairs (i, j) of nonnegative integers whose ternary expansions have no common digit 1 sorted first by i + j then by i.
%C This sequence is to Sierpinski carpet what A352909 is to Sierpinski gasket.
%C There are A293974(n + 1) pairs (i, j) with n = i + j.
%C See A362329 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 (0, 0),
%e (0, 1), (1, 0),
%e (0, 2), (2, 0),
%e (0, 3), (1, 2), (2, 1), (3, 0),
%e (0, 4), (1, 3), (2, 2), (3, 1), (4, 0),
%e (0, 5), (2, 3), (3, 2), (5, 0),
%e (0, 6), (1, 5), (2, 4), (4, 2), (5, 1), (6, 0),
%e (0, 7), (1, 6), (2, 5), (5, 2), (6, 1), (7, 0),
%e (0, 8), (2, 6), (6, 2), (8, 0),
%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, A352909, A362327 (i-values), A362328 (j-values), A362329 (complement).
%K nonn,tabf,base
%O 1,8
%A _Rémy Sigrist_, Apr 16 2023
|
