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The odd digits in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.
1

%I #10 Jul 26 2016 05:46:50

%S 1,2,3,5,4,6,7,9,10,8,11,13,12,15,17,20,19,31,33,21,35,37,39,22,23,51,

%T 53,55,57,24,25,59,71,73,75,14,26,27,77,79,91,16,28,29,93,95,97,99,

%U 110,40,41,111,113,115,117,42,43,119,131,133,112,44,45,135,137,139,151,114,46,47,153,155,157,159,171,18,48,49,173,175,177,179,191

%N The odd digits in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.

%C This is the lexicographically first such sequence starting with a(1)=1 and being always extended with the smallest integer not yet present that doesn't lead to a contradiction.

%H Eric Angelini, <a href="/A275375/b275375.txt">Table of n, a(n) for n = 1..1002</a>

%e The blocks of odd digits are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 5, 4, 6, 7,... which reproduces the sequence itself:

%e (1),2,(3,5),4,6,(7,9,1)0,8,(11,13,1)2,(15,17),20,(19,31,33),2(1,35,37,39),22,...

%Y Cf. A275375.

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 25 2016