A167507 -id:A167507 - cp's OEIS frontend

A006969 Number of characters in French ordinal numbers.

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

Offset: 1

N. J. A. Sloane, Simon Plouffe

Nombres de caractères (lettres, espaces et tirets) des nombres ordinaux en français.
In contrast to A196278, hyphens and spaces are counted here. First differs at n = 17 (dix-septième). - Georg Fischer, Aug 07 2021
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

			a(21) = # "vingt-et-unième" = 15, where # means length of the string.
a(50) = # "cinquantième" = 12.
a(80) = # "quatre-vingtième": the '-s' disappears from "quatre-vingts".
a(200) = # "deux-centième": the '-s' disappears from "deux cents".

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

Index entries for sequences related to number of letters in n

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

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

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

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

Edited by M. F. Hasler, Aug 08 2021

A139121 Total number of letters in the preceding terms spelled out in French.

Original entry on oeis.org

0, 4, 10, 13, 19, 26, 34, 46, 57, 70, 81, 94, 113, 123, 137, 151, 168, 184, 205, 217, 232, 250, 267, 287, 310, 322, 340, 357, 379, 403, 418, 435, 455, 478, 503, 516, 529, 546, 565, 585, 608, 619, 633, 651, 671, 692, 715, 729, 746, 765, 785, 808, 820, 833, 852, 873, 895, 920, 933, 952, 973, 995, 1020

Offset: 1

N. J. A. Sloane (based on Angelini's article), Jun 08 2008, Jun 15 2008

Form a sequence of French words as follows: look to the left, towards the beginning of the sequence and write down the number of letters you see; repeat; then replace the words by the corresponding numbers.
The sequence of words is: zero, quatre, dix, treize, dix-neuf, vingt-six, trente-quatre, quarante-six, cinquante-sept, ...
Hyphens, accents and spaces are not counted.
For an English version see A139097.

			The first word is "zero", because initially there are no letters to the left. The second word is "quatre" (and so a(2)=4), because at the end of the first word we can see four letters to the left. And so on.

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Cf. A005589, A060403, A139097.

A139121(n)={ n>1 & return( #select(Vec(French(n=A139121(n-1))),x->x>"@")+n )}  /* see A167507 for French() */  \\ M. F. Hasler, Sep 29 2011

Offset and a(9) corrected (according to wording of example) and terms beyond a(9) from M. F. Hasler, Sep 29 2011

A167508 Number of different letters in the French spelling of the number n.

Original entry on oeis.org

4, 2, 4, 5, 6, 4, 3, 4, 4, 4, 3, 4, 5, 5, 8, 6, 4, 7, 6, 7, 5, 7, 9, 8, 10, 7, 7, 8, 7, 8, 4, 5, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 9, 10, 7, 9, 10, 9, 9, 8, 8, 8, 10, 11, 9, 8, 10, 10, 9, 9, 8, 9, 10, 9, 11, 10, 8, 9, 10, 10, 9, 9, 11, 10, 12, 11, 9, 10, 11, 11, 10, 10, 12, 12, 10, 11, 12, 12, 11, 11, 12

Offset: 0

M. F. Hasler, Nov 18 2009

There is no number which can be written in French using only one letter, therefore the sequence does not contain the term 1.
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".
If an "e" with accent (as it occurs in "décillion") is considered as different from "e" without accent, then the range of the sequence should be { 2,3,...,26-3+1 }.

			The terms a(0),...,a(12) represent the number of characters in the strings "zéro", "un", "deux", "trois", "quatre", "cinq", "six", "sept", "huit", "neuf", "dix", "onze", "douze".
Since the "e" occurs twice in "treize", the number of different letters, a(13)=5, is less than the length of this string.
The same is true when the spelling contains hyphens as in "dix-sept" (a(17)=7) or spaces as in "vingt et un" (a(21)=9-2, since among the 9 nonblank characters, "t" and "n" occur twice).

Wiktionnaire, Annexe:Nombres de 1 à 100 en français (as of Nov. 18, 2009).

Cf. A167507.

import re
from num2words import num2words
from unidecode import unidecode
def A167508(n): return len(set(re.sub("[^a-z]", "", unidecode(num2words(n, lang='fr'))))) # Chai Wah Wu, Jun 13 2021

A167509 Least positive integer written with n different letters when spelled out in French.

Original entry on oeis.org

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

Offset: 2

M. F. Hasler, Nov 18 2009

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

			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.
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.

Wiktionnaire, Annexe:Nombres de 1 à 100 en français (as of Nov 18, 2009).

Cf. A167507, A080777, A134629.

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

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

A204593 Numbers having the same number of digits as letters when written in French.

Original entry on oeis.org

1000000000, 1000000000002, 1000000000005, 1000000000007, 1000000000008, 1000000000009, 1000000000011, 1000000000100, 3000000000000, 6000000000001, 10000000000006, 10000000000010, 11000000000001, 13000000000000, 15000000000000, 30000000000000, 100000000000006

Offset: 1

Eric Angelini, Feb 13 2012

Numbers such that A167507(n) = A055642(n). - M. F. Hasler, Feb 13 2012

			unmilliard
1000000000
unbilliondeux
1000000000002
unbillioncinq
1000000000005
unbillionsept
1000000000007
unbillionhuit
1000000000008
unbillionneuf
1000000000009
unbilliononze
1000000000011
unbillioncent
1000000000100
troisbillions
3000000000000
sixbillionsun
6000000000001
dixbillionssix
10000000000006
dixbillionsdix
10000000000010
onzebillionsun
11000000000001
treizebillions
13000000000000
quinzebillions
15000000000000
trentebillions
30000000000000
centbillionsun

E. Angelini, Table of n, a(n) for n = 1..107
Wiktionnaire, Annexe:Nombres en français.
E. Angelini, Terms a(1)...a(108) spelled out in French.

See A030455 for the (US) English version.

A075826 n minus (number of letters in English name of n).

Original entry on oeis.org

-4, -2, -1, -2, 0, 1, 3, 2, 3, 5, 7, 5, 6, 5, 6, 8, 9, 8, 10, 11, 14, 12, 13, 12, 14, 15, 17, 16, 17, 19, 24, 22, 23, 22, 24, 25, 27, 26, 27, 29, 35, 33, 34, 33, 35, 36, 38, 37, 38, 40, 45, 43, 44, 43, 45, 46, 48, 47, 48, 50, 55, 53, 54, 53, 55, 56, 58, 57, 58, 60, 63

Offset: 0

Jon Perry, Oct 14 2002

a(n) < 0 for n < 4, a(n) = 0 for n = 4 and a(n) > 0 for n > 4. - Bernard Schott, Feb 11 2020

The French variant would be n - A167507(n) = (-4, -1, -2, -2, -2, 1, 3, 3, 4, 5, 7, 7, 7, 7, 6, 9, 11, ...). The German variant would be n - A007208(n) = (-3, -2, -1, 0, 1, 1, 1, 4, 5, 6, 8, 7, 5, 6, 7, 8, 9, 10, ...). - M. F. Hasler, Mar 02 2020

			Seven contains 5 letters, therefore a(7) = 7 - 5 = 2.

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See pages 49 and 214.

Cf. A005589.

A075826(n)=n-A005589(n) \\ M. F. Hasler, Mar 02 2020

a(n) = n - A005589(n). - Michel Marcus, Feb 11 2020

Corrected and extended by David W. Wilson, Jul 04 2005

A139356 Sequence describing the positions of the consonants when the sequence is written in French (version 1).

Original entry on oeis.org

4, 1, 5, 8, 9, 11, 12, 13, 16, 17, 20, 22, 23, 25, 28, 30, 31, 34, 36, 39, 41, 43, 44, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 61, 62, 64, 65, 66, 67, 68, 71, 72, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 89, 90, 91, 93, 94, 96, 97, 99, 100, 103, 105

Offset: 1

N. J. A. Sloane (based on Angelini's article), Jun 08 2008

The sequence depends on how the initial terms are selected - see the Angelini article for the precise definition.

Eric Angelini, Jeux de suites, in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Cf. A139212, A139357, A139358, A167507.

lista(n) = frconspos([4])(n)
frconspos(startseq) = n -> {
my(consonants = Vec("bcdfghjklmnpqrstvwxyz"), charoffset = 0, seqindex = #startseq + 1, seq = Vec(startseq, n));
if(n <= #startseq, seq[1..n], for(i = 1, n, my(thisfrench = Vec(strchr([c|c<-Vecsmall(French(seq[i])), c>96])), consonantindexes = select(x->setsearch(consonants, x), thisfrench, 1));
for(j = 1, #consonantindexes, if(#select(I -> I == consonantindexes[j] + charoffset, startseq) == 0, if(seqindex + j - 1 <= n, seq[seqindex] = consonantindexes[j] + charoffset; seqindex++)));
charoffset += #thisfrench);
seq)}
/* see A167507 for French() */
\\ Tyler Busby, Dec 31 2022

a(12) corrected and more terms from Tyler Busby, Dec 31 2022

A196278 Number of letters in the French ordinal numbers.

Original entry on oeis.org

7, 8, 9, 9, 9, 7, 8, 8, 8, 7, 7, 8, 9, 11, 9, 8, 11, 11, 11, 9, 13, 13, 14, 14, 14, 12, 13, 13, 13, 9, 14, 14, 15, 15, 15, 13, 14, 14, 14, 11, 16, 16, 17, 17, 17, 15, 16, 16, 16, 12, 17, 17, 18, 18, 18, 16, 17, 17, 17, 11, 16, 16, 17, 17, 17, 15, 16, 16, 16, 15, 17, 16, 17, 19, 17, 16, 19, 19, 19, 15, 17, 19, 20, 20, 20, 18, 19, 19, 19, 18, 18, 19, 20, 22, 20, 19, 22, 22, 22, 8

Offset: 1

M. F. Hasler, Sep 30 2011

The first term corresponds to the masculine form "premier"; it could as well have been chosen to be "première". In contrast to A006969, hyphens and spaces are not counted. First differs at n = 17, where the hyphen in "dix-septième" is not counted here, but there.

It would be nice to have short programs in various languages to spell out the n-th ordinal number in French.

			a(1) = #"premier" = 7, a(2) = #"deuxième" = 8, a(3) = #"troisième" = 9,
a(4) = #"quatrième" = 9, a(5) = #"cinquième" = 9, a(6) = #"sixième" = 7, etc.
a(80) = 15, the number of letters in "quatre-vingtième". - _M. F. Hasler_, Aug 08 2021

Team of "ParisByPod", French ordinal numbers, 1 to 100, as of Sept. 2011.
Wiktionnaire, Ordinaux en français, Accord orthographique en nombre, quatre-vingtième.
Yale University Library, The names of numbers in French, German, Italian, and Spanish.

Cf. A006969, A080519, A167507.

Cf. A006944 (in American English).

A227865 Ending letter of a(n) equals starting letter of a(n+1), when spelled out in French; always choose the smallest possible number not yet used and not ending the sequence.

Original entry on oeis.org

0, 11001, 900, 7, 3, 61, 901, 903, 63, 65, 41, 905, 43, 67, 31, 907, 33, 68, 35, 45, 47, 37, 38, 300, 77, 301, 908, 303, 78, 305, 48, 307, 308, 317, 318, 320, 321, 917, 323, 600, 601, 918, 325, 80, 603, 605, 81, 920

Offset: 1

M. F. Hasler, Nov 01 2013

French version of a variant of A230862 without monotonicity.

No term must end in "deux", "quatre", "six", "neuf", "dix", "onze", "douze", "treize", "quatorze", "quinze", "seize", "trente", "quarante", "cinquante", "soixante", "mille", since there is no corresponding initial. The only possible endings are "zero", "un", "trois", "cinq", "(dix-)sept", "(dix-)huit", "vingt", "quatre-vingts", "cent(s)" and "million(s)" etc. This further reduces the possible initials to "n", "o", "q", "t", "s", with corresponding words: "neuf", "onze", "quatre/quatorze/quarante/quatre-vingt(s)", "trois/treize/trente" and "six/sept/seize/soixante(-dix)" (plus huge numbers like trillion, quadrillion, ...).

			zérO, Onze mille uN, Neuf centS, SepT, TroiS, Soixante-et-uN, Neuf cent uN, Neuf cent troiS, Soixante-troiS, Soixante-cinQ, Quarante-et-uN, Neuf cent cinQ, Quarante-troiS, Soixante-sepT, Trente-et-uN, Neuf cent sepT, Trente-TroiS, Soixante-huiT, Trente-cinQ, Quarante-cinQ, Quarante-sepT, Trente-sepT, Trente-huiT, Trois centS, Soixante-dix-sepT, Trois cent uN, Neuf cent huiT, Trois cent troiS, Soixante-dix-huiT, Trois cent cinQ, Quarante-huiT, Trois cent sepT, Trois cent huiT, Trois cent dix-sepT, Trois cent dix-huiT, Trois cent vingT, Trois cent vingt et uN, Neuf cent dix-sepT, Trois cent vingt-troiS, Six centS, Six cent uN, Neuf cent dix-huiT, Trois cent vingt-cinQ, Quatre-vingtS, Six cent troiS, Six cent cinQ, Quatre-vingt-uN, Neuf cent vingT, ...

Cf. A230862.

spellout(seq)={ for(i=1,#seq,my(s=Vecsmall(French(seq[i])));s[1]-=32;s[#s]-=32;print1(Strchr(s)","))} /* see A167507 for French() */

A233186 a(n) is the least number not smaller than the total number of letters in the French names for all terms up to and including a(n).

Original entry on oeis.org

5, 8, 15, 20, 28, 38, 50, 60, 66, 80, 95, 100, 106, 116, 128, 140, 156, 175, 195, 206, 220, 236, 256, 279, 300, 301, 315, 330, 350, 369, 395, 409, 428, 450, 469, 496, 506, 520, 536, 556, 579, 600, 601, 606, 620, 635, 655, 676, 700, 701, 706, 720, 736, 756, 776, 800, 801, 806, 820, 836, 856, 879, 900, 901, 910, 926, 945, 965, 988

Offset: 1

Eric Angelini and M. F. Hasler, Dec 05 2013

A variant of A233185 and the English version A233184. Whereas in the English case the use of the weak inequality would only change the first, third and fourth term (credits to H. Havermann), there are more differences between the two variants in the French version. See A233187-A233188 for German variants.

E. Angelini, Cumulative quantity of letters used in a list of English number-names, SeqFan list, Dec 05 2013

a=0;k=0;for(n=1,99,until( k++ >= a + A167507(k),); print1(k,","); a+=A167507(k))

cp's OEIS Frontend

A006969 Number of characters in French ordinal numbers.

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A139121 Total number of letters in the preceding terms spelled out in French.

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A167508 Number of different letters in the French spelling of the number n.

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A167509 Least positive integer written with n different letters when spelled out in French.

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A204593 Numbers having the same number of digits as letters when written in French.

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A075826 n minus (number of letters in English name of n).

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A139356 Sequence describing the positions of the consonants when the sequence is written in French (version 1).

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A196278 Number of letters in the French ordinal numbers.

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