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.

%I A362329 #4 Apr 20 2023 09:00:03
%S A362329 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 A362329 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 A362329 4,13,5,12,7,10,10,7,12,5,13,4,14,3,16,1
%N A362329 Pairs (i, j) of nonnegative integers whose ternary expansions have a common digit 1 sorted first by i + j then by i.
%C A362329 This sequence is to Sierpinski carpet what A353296 is to Sierpinski gasket.
%C A362329 There are n + 1 - A293974(n + 1) pairs (i, j) with n = i + j.
%C A362329 See A362326 for the other pairs.
%H A362329 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_carpet">Sierpiński carpet</a>
%e A362329 The first pairs are:
%e A362329     (1, 1),
%e A362329     (1, 4), (4, 1),
%e A362329     (3, 3),
%e A362329     (3, 4), (4, 3),
%e A362329     (1, 7), (3, 5), (4, 4), (5, 3), (7, 1),
%e A362329     (4, 5), (5, 4),
%e A362329     (5, 5),
%e A362329     (1, 10), (4, 7), (7, 4), (10, 1),
%e A362329     ...
%o A362329 (PARI) is(i, j) = { while (i && j, if (i%3==1 && j%3==1, return (0), i\=3; j\=3;);); return (1); }
%o A362329 row(ij) = apply (i -> [i, ij-i], select(i -> !is(i, ij-i), [0..ij]))
%Y A362329 Cf. A293974, A353296, A362326 (complement), A362330 (i-values), A362331 (j-values).
%K A362329 nonn,tabf,base
%O A362329 1,4
%A A362329 _Rémy Sigrist_, Apr 16 2023