A284651 Lexicographically earliest sequence of unique numbers such that for each digit "d" exactly one of the gaps to the neighboring digits "d" is equal to d, and no gap is smaller than d.

1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 132, 91, 21, 34, 25, 32, 46, 15, 17, 23, 621, 31, 72, 41, 213, 42, 53, 26, 47, 58, 94, 63, 171, 38, 19, 12, 35, 27, 36, 85, 14, 176, 248, 29, 51, 71, 265, 28, 97, 16, 100, 48, 37, 54, 39, 625, 724, 86, 294, 200, 78, 45, 161, 475, 92, 61, 214, 57, 89, 415, 137, 68, 300

Offset

1,2

Comments

The sequence is started with a(1) = 1 and always extended with the smallest integer not yet present and not leading to a contradiction. This sequence is a variant of A284516 and the variant is explained in the "Example" section.

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Example

The first 16 terms of this variant are 1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 132.
The first 16 terms of the orig seq are 1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 131.
The difference is in the last digit of the last term (131 becomes here 132): in the original sequence the first digit "1" of the term "131" is twice at a gap of 1 digit from another "1" (there is indeed a gap of 1 digit between the first "1" of "131" and the "1" of "18" AND there is also a gap of 1 digit between the first and the second "1" of "131"). This is forbidden in this variant, whatever digit "d" you pick: if your digit "d" is at a gap of d from another "d", it cannot be at the same gap of another "d".

Crossrefs

Sequence in context: A090526 A362433 A284516 * A031038 A017413 A194887

Adjacent sequences: A284648 A284649 A284650 * A284652 A284653 A284654

Keyword

nonn,base

Author

Lars Blomberg and Eric Angelini, Mar 31 2017

Status

approved