

A319921


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.


2



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
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OFFSET

1,1


COMMENTS

By construction, all integers have here an odd number of digits and an odd number of letters in their French translation.


REFERENCES

Eric Angelini, Maths étonnant, tangente, No. 189, juilletaoût 2019, p. 29.


LINKS

JeanMarc 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.


EXAMPLE

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.


CROSSREFS

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


KEYWORD

base,nonn,word


AUTHOR

Eric Angelini and JeanMarc Falcoz, Oct 01 2018


STATUS

approved



