A299823 To concatenate all terms, to concatenate the odd rank terms or to concatenate the even rank terms produces the same result.

12, 121, 1, 2, 21, 11, 122, 22, 111, 1111, 1222, 222, 211, 2111, 11111, 111112, 12222, 2222, 2221, 221, 1211, 12111, 111111, 1111111, 1111121, 1112, 22222, 122222, 222222, 2222221, 1221, 2211, 121112, 21112, 11111111, 111111111, 1111111111, 11111111111, 11121

Offset

1,1

Comments

The sequence starts with a(1) = 12 and is always extended with the smallest integer not yet present and not leading to a contradiction.

This is the lexicographically first sequence having this property, except the trivial 1, 11, 111, 1111, 11111,...

Trying a(1) = 10 gives a sequence with terms having leading zeroes -- which is not admitted.

All terms belong to A007931. - Rémy Sigrist, Dec 08 2018

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 100000 terms

Rémy Sigrist, Perl program for A299823

Example

The first five terms of the sequence are:
12,121,1,2,21
The first five odd-ranked terms are:
12,1,21,122,111
The first five even-ranked terms are:
121,2,11,22,1111
... and we see that those three partitions start with the same concatenation:
121211221...

Prog

(Perl) See Links section.

Crossrefs

Cf. A007931.

Sequence in context: A262204 A037097 A337202 * A222634 A018204 A176779

Adjacent sequences: A299820 A299821 A299822 * A299824 A299825 A299826

Keyword

nonn,base,look

Author

Eric Angelini, Feb 19 2018

Extensions

More terms from Rémy Sigrist, Dec 08 2018

Status

approved