A167509 Least positive integer written with n different letters when spelled out in French.

1, 6, 2, 3, 4, 17, 14, 22, 24, 53, 74, 92, 97

Offset

2,2

Comments

There is no number which can be written in French using only one letter, therefore the sequence starts at offset n=2, cf. examples.

A variant of the definition would be the "least nonnegative integer ....", in which case a(4)=0 ("zéro" with "accent aigu" on the "e"), all other terms remaining the same.

It appears that letters "j", "k" and "w" don't occur in any number, while "m" and "l" first occur in "mille" (=1000), and "b" first occurs in "billion".

If an "é" with accent (as it occurs in "décillion") is considered as different from "e" without accent, the sequence should have 26-3+1 terms.

Links

Table of n, a(n) for n=2..14.

Wiktionnaire, Annexe:Nombres de 1 à 100 en français (as of Nov 18, 2009).

Formula

a(n) = min { k | A167508(k) = n }

Example

The terms a(2),...a(14) correspond to the French words un, six, deux, trois, quatre, dix-sept, quatorze, vingt-deux, vingt-quatre, cinquante-trois, soixante-quatorze, quatre-vingt-douze, quatre-vingt-dix-sept.
Here, "vingt-quatre" is the first term which contains a letter occurring twice, and therefore has a length greater than n; we conjecture that this is the case for all subsequent terms.

Prog

(PARI) A167509(n) = { for( k=1, #A167508, A167508[k]==n & return(k)); error("Found no result for n="n) }

Crossrefs

Cf. A167507, A080777, A134629.

Sequence in context: A330531 A374645 A134105 * A011362 A090425 A160081

Adjacent sequences: A167506 A167507 A167508 * A167510 A167511 A167512

Keyword

fini,nonn,word

Author

M. F. Hasler, Nov 18 2009

Status

approved