A375232 Two terms that contain the digit "d" are always separated by "d" terms that do not contain the digit "d". This is the lexicographically earliest sequence of distinct nonnegative integers with this property.

0, 10, 20, 100, 30, 102, 40, 101, 203, 105, 60, 1024, 300, 107, 200, 150, 304, 1026, 80, 109, 230, 10457

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 06 2024

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is finite, there is no 23rd term.

Examples

			As we start the sequence with a(1) = 0, the digit 0 must be present in every term of the sequence.
We extend it now with a(2) = 10 as 10 is the smallest integer not present that contains the digit 0.
The next term will be a(3) = 20 as 20 is the smallest integer not present that contains the digit 0.
The next term will be a(4) = 100 as 100 is the smallest integer not present that contains both the digits 0 and 1.
The next term will be a(5) = 30 as 30 is the smallest integer not present that contains the digit 0.
The next term will be a(6) = 102 as 102 is the smallest integer not present that contains the digits 0, 1 and 2.
The next term will be a(7) = 40 as 40 is the smallest integer not present that contains the digit 0.
The next term will be a(8) = 101 as 101 is the smallest integer not present that contains both the digits 0 and 1.
Etc.
		

Links

• Eric Angelini, Digits and gaps, personal blog of the author.

Crossrefs

Cf. A284516.

Extensions

a(14) and successive terms computed by Michael S. Branicky.