A362326
Pairs (i, j) of nonnegative integers whose ternary expansions have no common digit 1 sorted first by i + j then by i.
Original entry on oeis.org
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, 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, 0, 9, 1, 8, 2, 7, 3, 6, 6, 3, 7, 2, 8, 1, 9, 0, 0, 10
Offset: 1
The first pairs are:
(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), (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),
...
-
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]))
A362328
The j-values of pairs (i, j) listed in A362326.
Original entry on oeis.org
0, 1, 0, 2, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 3, 2, 0, 6, 5, 4, 2, 1, 0, 7, 6, 5, 2, 1, 0, 8, 6, 2, 0, 9, 8, 7, 6, 3, 2, 1, 0, 10, 9, 8, 7, 6, 4, 3, 2, 1, 0, 11, 9, 8, 6, 5, 3, 2, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
Offset: 1
-
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 -> ij-i, select(i -> is(i, ij-i), [0..ij]))
A363930
Irregular table T(n, k), n >= 0, k = 1..A363710(n), read by rows; the n-th row lists the nonnegative numbers m <= n such that A003188(m) AND A003188(n-m) = 0 (where AND denotes the bitwise AND operator).
Original entry on oeis.org
0, 0, 1, 0, 2, 0, 3, 0, 1, 3, 4, 0, 1, 4, 5, 0, 6, 0, 7, 0, 1, 7, 8, 0, 1, 2, 3, 6, 7, 8, 9, 0, 2, 3, 7, 8, 10, 0, 3, 8, 11, 0, 1, 3, 9, 11, 12, 0, 1, 12, 13, 0, 14, 0, 15, 0, 1, 15, 16, 0, 1, 2, 3, 14, 15, 16, 17, 0, 2, 3, 4, 6, 12, 14, 15, 16, 18, 0, 3, 4, 7, 12, 15, 16, 19
Offset: 0
Table T(n, k) begins:
n n-th row
-- ----------------------
0 0
1 0, 1
2 0, 2
3 0, 3
4 0, 1, 3, 4
5 0, 1, 4, 5
6 0, 6
7 0, 7
8 0, 1, 7, 8
9 0, 1, 2, 3, 6, 7, 8, 9
10 0, 2, 3, 7, 8, 10
11 0, 3, 8, 11
12 0, 1, 3, 9, 11, 12
13 0, 1, 12, 13
14 0, 14
15 0, 15
16 0, 1, 15, 16
-
row(n) = { select (m -> bitand(bitxor(m, m\2), bitxor(n-m, (n-m)\2))==0, [0..n]) }
Showing 1-3 of 3 results.
Comments