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%I #17 Dec 20 2023 08:04:32
%S 331,233,10177,224,10314,10323,210,203,110,10717,84700,420,121,340,
%T 311,206,236,10182,10454,112,302,99300,10217,10331,10206,212,103,326,
%U 10033,136,216,217,305,218,10084,270,117,470,1008224,43400,170,11000,10024,21400,14201,307,410,10210,313,332,1004644,10066,10304,32100,10184,122
%N Underline the central digit of all terms: the underlined digits reconstruct the starting sequence. This is also true if one translates the sequence in French and underlines the central letter of each word: the underlined letters spell the (French) sequence again. This is the lexicographically earliest sequence of distinct terms.
%C By construction, all integers have here an odd number of digits and an odd number of letters in their French translation.
%H Jean-Marc Falcoz, <a href="/A319921/b319921.txt">Table of n, a(n) for n = 1..1001</a>
%H Eric Angelini, <a href="https://tangente-mag.com/maths_etonnantes.php?id=4747">Des suites inouïes</a>, Maths étonnantes, Tangente, No. 189, juillet-août 2019, p. 29.
%H Nicolas Graner, <a href="https://www.graner.net/nicolas/nombres/nom.php">Les grands nombres en français</a>. This link explains why the authors didn't take into account the letters B, J, K, W and Y.
%e The sequence starts with 331, 233, 10177, 224, 10314, and the central (underlined) digits are 3,3,1,2,3,... which are precisely the digits starting the sequence itself; now the successive 5 unique central letters of the above 5 French terms are T, R, O, I, S and this spells the beginning of TROIS CENT TRENTE ET UN, the term a(1).
%e The first term diverging from A319718 is a(21) = [TROISC(E)NTDEUX, 302] as a(21) is the smallest integer > a(16) = [DEUXC(E)NTSIX, 206], both having a central (underlined) letter E.
%Y Cf. A319718 (repeated terms are allowed, in contrast to this sequence)
%K base,nonn,word
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Oct 01 2018