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Number of characters in French ordinal numbers.
(Formerly M4334)
3

%I M4334 #45 Aug 14 2021 15:11:04

%S 7,8,9,9,9,7,8,8,8,7,7,8,9,11,9,8,12,12,12,9,15,14,15,15,15,13,14,14,

%T 14,9,16,15,16,16,16,14,15,15,15,11,18,17,18,18,18,16,17,17,17,12,19,

%U 18

%N Number of characters in French ordinal numbers.

%C Nombres de caractères (lettres, espaces et tirets) des nombres ordinaux en français.

%C In contrast to A196278, hyphens and spaces are counted here. First differs at n = 17 (dix-septième). - _Georg Fischer_, Aug 07 2021

%C In French the final -s in "quatre-vingts", "deux cents", ... disappears when the ordinal suffix "-ième" is appended. (This is currently incorrectly handled in the Python module num2words.) Also, the trailing "-e" of numbers ending in "quatre", "onze" - "seize", "trente" - "soixante" disappears. Therefore, in all these cases the name of the ordinal has only 3 letters more than the name of the cardinal, viz. a(n) = A007005(n)+3. For numbers ending in "cinq", there appears an additional "u", whence a(n) = A007005(n)+5 in this case. - _M. F. Hasler_, Aug 08 2021

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H <a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a>

%F a(n) = A007005(n) + e, where e = 4 except for n = 1 and when the French name of n ends in "cinq" (then e = 5), or when it ends in "-e" or "-ts" (then e = 3). - _M. F. Hasler_, Aug 08 2021

%e a(21) = # "vingt-et-unième" = 15, where # means length of the string.

%e a(50) = # "cinquantième" = 12.

%e a(80) = # "quatre-vingtième": the '-s' disappears from "quatre-vingts".

%e a(200) = # "deux-centième": the '-s' disappears from "deux cents".

%o (PARI) apply( {A006969(n, t=French(n))=#t+if(n==1||"nq"==t=Strchr(Vecsmall(t)[-2..-1]), 5, "ts"==t || Vec(t)[2]=="e", 3, 4)}, [1..55]) \\ See A007005 for French(). - _M. F. Hasler_, Aug 08 2021

%Y Cf. A006944 (in American English), A196278 (similar, but not counting spaces and hyphens).

%Y Cf. A007005, A167507 (number of letters/characters in French name of n).

%K nonn,word

%O 1,1

%A _N. J. A. Sloane_, _Simon Plouffe_

%E Edited by _M. F. Hasler_, Aug 08 2021