A358054 Starting with 0, smallest integer not yet in the sequence such that no two neighboring digits differ by 1.

0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 90, 80

Offset: 0

Author

Gavin Lupo and Eric Angelini, Oct 28 2022

Keywords

• nonn
• base
• easy

Comments

Integers such as 10, 12, 21, 76, 6792, and 10744 (see A082927) will not appear in the sequence as they contain adjacent digits that differ by 1. Some integers may be disallowed only temporarily; for example, if a(n) = 79, and all nonnegative integers < 79 are already in the sequence, then a(n+1) = 90, because a(n+1) must not start with an 8, as it would differ by 1 from the digit "9" in 79. Now, a(n+2) can equal 80.

Examples

			a(0) = 0.
a(1) = 2. Cannot be 1. Smallest integer that can be placed = 2.
a(2) = 4. Cannot be 1 or 3. Smallest integer that can be placed = 4.
a(3) = 1. Cannot be 3 or 5. Smallest integer that can be placed = 1.
...
(Nonnegative integers < 86, disregarding invalid integers, have already appeared.)
a(74) = 86.
a(75) = 88. Cannot be 87, as it contains adjacent digits that differ by 1. Smallest integer that can be placed = 88.
a(76) = 111. Cannot be 89, 90->99 (9 and 8 differ by 1), or 100->110 (1 and 0 are adjacent and differ by 1). Smallest integer that can be placed = 111.
		

Links

• Gavin Lupo, Table of n, a(n) for n = 0..5000
• David A. Corneth, PARI program

Crossrefs

Cf. A082927, A219250.

Programs

PARI

\\ See PARI link \\ David A. Corneth, Oct 31 2022