OFFSET
1,2
COMMENTS
The terms are defined as follows. Start by choosing the initial terms: 1, 2, 3. Then write the rows of table A088643 backwards but always leave off the last three quarters of the terms. This gives: [], [], [], [1], [1], [1], [1], [1, 2], [1, 2], [1, 2], [1, 4], [1, 4, 3,], [1, 4, 3] etc. Then build the sequence up by repeatedly choosing the first such truncated row that extends the terms already chosen. [Edited by Peter Munn, Aug 19 2021]
It is not until the 26th truncated row - [1, 2, 3, 4, 7, 6] - that the initial list is extended at all. It is unclear whether this process can be continued indefinitely, although I have verified by computer that it generates a sequence of at least 2000 terms. Conjecturally: (1) the sequence is infinite, (2) it is the unique sequence containing infinitely many complete rows of table A088643, and (3) for every n > 0 there exists N > 0 such that the first n terms of this sequence are contained in every row of table A088643 from the N-th onwards.
Maybe the idea could be expressed more concisely by defining this sequence as the limit of the reversed rows of A088643? - M. F. Hasler, Aug 04 2021
It seems we do not know of an existence proof for the limit of the reversed rows of A088643. - Peter Munn, Aug 19 2021
LINKS
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Boddington, Oct 30 2007, Mar 06 2010
EXTENSIONS
Name edited by Peter Munn, Aug 19 2021
STATUS
approved