A167507 Number of letters in the French spelling of the number n, not counting hyphens and spaces.

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

Offset: 0

Author

M. F. Hasler, Nov 18 2009

Keywords

• nonn
• word

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

Examples

			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 "dix-sept" (a(17)=7), or spaces as in "vingt et un" (a(21)=9).
		

Links

• Wiktionnaire, Annexe:Nombres de 1 à 100 en français (as of Nov. 18, 2009).
• Index entries for sequences related to names of numbers

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).

Programs

PARI

apply( {A167507(n)=#[0|c<-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","dix-sept","dix-huit","dix-neuf"][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( "quatre-vingt-", French( n-80 )));
n%10==0 & return( Str( ["vingt","trente","quarante","cinquante","soixante", "soixante-dix","quatre-vingts"][n\10-1] ));
Str( French((n\10-(n>70))*10), if(n%10==1," et ","-"), French(n%10+10*(n>70)))}
\\ M. F. Hasler, Nov 19 2009

Extensions

Keyword "fini" removed by M. F. Hasler, Nov 19 2009

a(80) and a(81) corrected by Bernard Schott, Feb 19 2020