cp's OEIS Frontend

A080519 Positions of the letter t in the French phrase enumerating these positions, "T est la première, quatrième, dix-huitième, trentième, trente-cinquième,... lettre dans cette phrase...".

%I A080519 #21 Jul 22 2025 05:53:43
%S A080519 1,4,18,30,35,39,44,48,59,63,79,84,96,101,113,129,131,146,162,169,173,
%T A080519 182,189,201,203,213,214,226,231,243,244,248,251,261,268,280,287,300,
%U A080519 307,320,327,329,341,345,352,364,368,375,391,393,407,408,424,425
%N A080519 Positions of the letter t in the French phrase enumerating these positions, "T est la première, quatrième, dix-huitième, trentième, trente-cinquième,... lettre dans cette phrase...".
%C A080519 The phrase ends "... où les espaces, les virgules et les traits d'union ne comptent pas." This means that spaces, commas and hyphens are not counted.
%C A080519 French version of A005224.
%H A080519 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Unieme.htm">27 phrases autoréférentes</a>.
%H A080519 Eric Angelini, <a href="/A080519/a080519.pdf">27 phrases autoréférentes</a> [Cached copy, included with permission of the author]
%e A080519 "T est la première, quatrième, dix-huitième, trentième, ... lettre de cette phrase..." has a 't' in 1st, 4th, 18th, 30th, ... position.
%e A080519 But the dots represent an infinite list of words: In contrast to the versions starting with another letter (except for 'e', 'i' and 'm' which share this property), the phrase cannot be finite, because each term adds at least 2 't's on the average. This will remain true even after reaching "mille" (thousand), "un million", "un milliard", ... because these t-less words occur almost always accompanied by coefficients between 1 and 1000.
%o A080519 (PARI) {c=0; apply(x -> x>"@" & c++ & x=="t" & print1(c","), Vec("t est la premiere, quatrieme, dix-huitieme, trentieme, trente-cinquieme, trente-neuvieme, quarante-quatrieme, quarante-huitieme, cinquante-neuvieme, soixante-troisieme, soixante-dix-neuvieme, quatre-vingt-quatrieme, quatre-vingt-seizieme, cent et unieme, cent treizieme, cent vingt-neuvieme cent trente et unieme, cent quarante-sixieme, cent soixante-deuxieme, cent soixante-neuvieme, cent soixante-treizieme, cent quatre-vingt-deuxieme, cent quatre-vingt-neuvieme, deux cent et unieme, deux cent troisieme, deux cent treizieme,..."));}  \\ _M. F. Hasler_, Sep 30 2011
%Y A080519 Cf. Aronson's sequence A005224, A080517-A080520.
%K A080519 nonn,word
%O A080519 1,2
%A A080519 _N. J. A. Sloane_, Mar 21 2003