A167509 - OEIS

%I #11 Jan 12 2019 08:06:18

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

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

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

%C 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.

%C 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".

%C 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.

%H Wiktionnaire, <a href="http://fr.wiktionary.org/wiki/Annexe:Nombres_de_1_%C3%A0_100_en_fran%C3%A7ais">Annexe:Nombres de 1 à 100 en français</a> (as of Nov 18, 2009).

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

%e 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.

%e 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.

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

%Y Cf. A167507, A080777, A134629.

%K fini,nonn,word

%O 2,2

%A _M. F. Hasler_, Nov 18 2009