

A299823


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


1



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
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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 oddranked terms are:
12,1,21,122,111
The first five evenranked 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



