

A167507


Number of letters in the French spelling of the number n, not counting hyphens and spaces.


22



4, 2, 4, 5, 6, 4, 3, 4, 4, 4, 3, 4, 5, 6, 8, 6, 5, 7, 7, 7, 5, 9, 9, 10, 11, 9, 8, 9, 9, 9, 6, 10, 10, 11, 12, 10, 9, 9, 10, 10, 8, 12, 12, 13, 14, 12, 11, 12, 12, 12, 9, 13, 13, 14, 15, 13, 12, 13, 13, 13, 8, 12, 12, 13, 14, 12, 11, 12, 12, 12, 11, 12, 13, 14, 16, 14, 13, 15, 15, 15, 12, 13
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OFFSET

0,1


COMMENTS

Sequence A007005 is a variant of this sequence, where spaces and hyphens are counted.
In most languages, there exists a number N after which all numbers are written with fewer letters than the number itself. In English, in German and in French, N = 4. Here, if n > 4, then a(n) < n, and if n <= 4, then a(n) > n.  Bernard Schott, Jan 11 2019


LINKS

Table of n, a(n) for n=0..81.
Wiktionnaire, Annexe:Nombres de 1 à 100 en français (as of Nov. 18, 2009).
Index entries for sequences related to names of numbers


EXAMPLE

The terms a(0),...,a(16) represent the number of characters in the strings "zéro", "un", "deux", "trois", "quatre", "cinq", "six", "sept", "huit", "neuf", "dix", "onze", "douze", "treize", "quatorze", "quinze", "seize".
Since spaces and punctuation are not counted, a(n) is less than the length of the character string whenever the spelling of n contains hyphens, as in "dixsept" (a(17)=7), or spaces as in "vingt et un" (a(21)=9).


PROG

(PARI) apply( {A167507(n)=#[0c<Vecsmall(French(n)), c>96]}, [0..81]) \\ updated by M. F. Hasler, Feb 19 2020 [If old versions of PARI/gp give an error, use e.g. Vec(Vecsmall...).]
/* Helper function: spell out n in French. Extended to 10^24 (now further extensible via the 2nd optional argument) for A204593 on Feb 16 2012. */
French(n, t=[10^18, "trillion", /*10^15, "billiard", */ 10^12, "billion", 10^9, "milliard", 10^6, "million"])={ if( n>999, n>=10^6*t[1] & error(n" is too large  this implementation is restricted to n < 10^", 5+#Str(t[1])); forstep(i=1, #t, 2, n\t[i] & return(Str(French(n\t[i])" "t[i+1], if(n\t[i]>1, "s", ""), if(n%t[i], Str(" "French(n%t[i])), "")))); return(Str(if(n\1000>1, Str(French(n\1000), " "), ""), "mille", if(n%1000, Str(" ", French(n%1000)), ""))));
n<20 & return([ "zero", "un", "deux", "trois", "quatre", "cinq", "six", "sept", "huit", "neuf", "dix", "onze", "douze", "treize", "quatorze", "quinze", "seize", "dixsept", "dixhuit", "dixneuf"][n+1]);
n >= 100 & return( Str( if( n>199, Str(French(n\100), " "), ""), "cent", if(n%100, Str(" ", French(n%100)), if(n>199, "s", "")/*deux cents*/)));
n > 80 & return( Str( "quatrevingt", French( n80 )));
n%10==0 & return( Str( ["vingt", "trente", "quarante", "cinquante", "soixante", "soixantedix", "quatrevingts"][n\101] ));
Str( French((n\10(n>70))*10), if(n%10==1, " et ", ""), French(n%10+10*(n>70)))}
\\ M. F. Hasler, Nov 19 2009


CROSSREFS

Cf. A005589 (English analog), A167508 (counts distinct letters).
Cf. A001050 (Finnish analog), A006994 (Russian analog), A007208 (German analog), A011762 (Spanish analog), A026858 (Italian analog).
Sequence in context: A224183 A131953 A167508 * A007005 A237869 A066978
Adjacent sequences: A167504 A167505 A167506 * A167508 A167509 A167510


KEYWORD

nonn,word


AUTHOR

M. F. Hasler, Nov 18 2009


EXTENSIONS

Keyword "fini" removed by M. F. Hasler, Nov 19 2009
a(80) and a(81) corrected by Bernard Schott, Feb 19 2020


STATUS

approved



