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A167507
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Number of letters in the French spelling of the number n, not counting hyphens and spaces.
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25
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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
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0,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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).
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PROG
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(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)))}
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CROSSREFS
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KEYWORD
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nonn,word
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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