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.

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

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Oct 01 2018

Keywords

• base
• nonn
• word

Comments

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

Examples

			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.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..1001
• Eric Angelini, Des suites inouïes, Maths étonnantes, Tangente, No. 189, juillet-août 2019, p. 29.
• 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.

Crossrefs

Cf. A319718 (repeated terms are allowed, in contrast to this sequence)