A319032 Length of segments delimited by the letter "u" when the sequence is spelled out in French.

1, 6, 8, 5, 8, 9, 3, 8, 5, 9, 8, 5, 8, 9, 3, 9, 3, 8, 9, 3, 8, 5, 9, 8, 5, 9, 8, 5, 8, 5, 9, 8, 5, 8, 9, 3, 9, 3, 8, 9, 3, 9, 3, 8, 9, 3, 8, 9, 3, 9, 3, 8, 9, 3, 8, 5, 9, 8, 5, 9, 8, 5, 8, 5, 9, 8, 5, 9, 8, 5, 8, 5, 9, 8, 5, 8, 5, 9, 8, 5, 9, 8, 5, 8, 5, 9, 8, 5, 8, 9, 3, 9, 3, 8, 9, 3, 9, 3, 8, 9

Offset: 1

Author

Eric Angelini, Sep 08 2018

Keywords

• nonn
• word

Comments

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|, ...

Crossrefs

Cf. A230763 for an English sequence with segments delimited by the letter "e" and A243992 for a base-10 sequence with segments delimited by the digit "1".