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

1,2

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|, ...

Links

Table of n, a(n) for n=1..100.

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".

Sequence in context: A260691 A296845 A030644 * A344125 A073462 A231095

Adjacent sequences: A319029 A319030 A319031 * A319033 A319034 A319035

Keyword

nonn,word

Author

Eric Angelini, Sep 08 2018

Status

approved