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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 11:38 EDT 2022. Contains 355985 sequences. (Running on oeis4.)