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A319921
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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.
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2
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331, 233, 10177, 224, 10314, 10323, 210, 203, 110, 10717, 84700, 420, 121, 340, 311, 206, 236, 10182, 10454, 112, 302, 99300, 10217, 10331, 10206, 212, 103, 326, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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By construction, all integers have here an odd number of digits and an odd number of letters in their French translation.
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REFERENCES
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Eric Angelini, Maths étonnant, tangente, No. 189, juillet-août 2019, p. 29.
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LINKS
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Jean-Marc Falcoz, Table of n, a(n) for n = 1..1001
Nicolas Graner, Les grands nombres en français. This link explains why the authors didn't take into account the letters B, J, K, W and Y.
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EXAMPLE
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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).
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.
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CROSSREFS
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Cf. A319718 (repeated terms are allowed, in contrast to this sequence)
Sequence in context: A140908 A256586 A319718 * A179400 A139657 A140000
Adjacent sequences: A319918 A319919 A319920 * A319922 A319923 A319924
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KEYWORD
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base,nonn,word
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AUTHOR
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Eric Angelini and Jean-Marc Falcoz, Oct 01 2018
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STATUS
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approved
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