Sequence of integers that contains all combinations of digits with no repeating digits

Question

What is the name of the infinite sequence of positive integers in some base n that contain all possible combinations of digits with no repeating consecutive digits and do not begin with zero?

For example:
In base $2$: $1, 10, 101, 1010, 10101, 101010...$
In base $3$: $1, 2, 10, 12, 20 ,21, 101, 102, 120, 121, 201, 202, 210, 212, 1010, 1012... $
In base 4: $1, 2, 3, 10, 12, 13, 20, 21, 23, 30, 31, 32, 101, 102, 103, 120...$

Obviously, the sequence is specific to its base. For example, in binary the number $10101010101010$ belongs in the sequence, however in decimal this number is equal to $10922$, which is not allowed in the sequence, because it contains two consecutive $2$'s.

I suppose, the question can be rephrased in terms of all possible sets with unique order of a certain number of unique elements such that no element can be put next to a same element and that the first element cannot be put in the first place.

Answer 1

These sequences appear at OEIS.org as

• A000975 (base 2)
• A031941 (base 3)
• A031942 or A043090 (base 4)
• A031943 or A043091 (base 5)
• A043092 ... A043096 (base 6 through base 10)

They are not named, and no references are given, so it is unlikely that they have been named.