cp's OEIS Frontend

Cut the sequence of digits of the concatenation of all terms after each odd digit: 1|23|465|8207|222421|26289|40424423|46..., then the length of the segments is given by the sequence itself. This defines the sequence, with the additional requirements that no number can appear more than once, and that the smallest possible term must always be chosen.

There cannot be two odd digits in a row, which excludes many numbers such as 11, 13, 15, .... Moreover, after the initial terms, no "small" numbers with more than one odd digit can be present. Therefore this cannot be a permutation of the integers, and numbers with odd digit(s) (and, in particular, primes) become increasingly sparse.

See A230765 for the "dual" version where chunks of odd digits are delimited by an even digit.

See A230763 for a version where, instead of digits, the English spelling of the terms is considered.

Translate the sequence S to French, to get French(S) = UN, SIX, HUIT, CINQ, HUIT, NEUF, TROIS, HUIT, CINQ, NEUF, HUIT, CINQ, HUIT, NEUF, TROIS, NEUF, TROIS, HUIT, NEUF, TROIS, HUIT, CINQ, NEUF, ...

Then insert a stroke immediately after each letter "U" of S: U|N, SIX, HU|IT, CINQ, HU|IT, NEU|F, TROIS, HU|IT, CINQ, NEU|F, HU|IT, CINQ, HU|IT, NEU|F, TROIS, NEU|F, TROIS, HU|IT, NEU|F, TROIS, HU|IT, CINQ, NEU|F, ..."

Now the length of each chunk is given by the sequence S itself. In case of several possible choices compatible with this property, we require the smallest one to be chosen.

After the 2nd term, the only integers used are 3, 5, 8 and 9 in a seemingly chaotic order.

The author does not know if the sequence enters into a loop at some point. The shortest such known loop in French is [4,3,8] for segments delimited by the letter "T": QUAT|RE, T|ROIS, HUIT|, QUAT|RE, T|ROIS, HUIT|, QUAT|RE, T|ROIS, HUIT|, ...