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

Author

M. F. Hasler, Nov 18 2009

Keywords

• fini
• nonn
• word

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A167507, A080777, A134629.

Programs

PARI

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

Formula

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