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A229084 Lexicographically earliest sequence of distinct positive integers written in base 2 such that the concatenation of the terms equals the concatenation of the positive integers, and no term appears in its natural position.

%I A229084 #11 Sep 19 2013 16:14:12
%S A229084 110,1,1100,10,11,101,111000,100,11010,10111,1001,1011,1101,111,
%T A229084 100001000,110010,1001110,10010,10110,110101,1111000,110011,1010,
%U A229084 110111,11001,11011,1110,1111,1100000,10000,11000,101000,11100,100100,101100,110100,11110,1000
%N A229084 Lexicographically earliest sequence of distinct positive integers written in base 2 such that the concatenation of the terms equals the concatenation of the positive integers, and no term appears in its natural position.
%C A229084 Leading zeros are forbidden.
%C A229084 The positive integers written in base 10:
%C A229084 +-+--+--+---+---+---+---+----+----+----+----+----+----+----+
%C A229084 |1| 2| 3| 4 | 5 | 6 | 7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 |...
%C A229084 +-+--+--+---+---+---+---+----+----+----+----+----+----+----+
%C A229084 The positive integers written in base 2:
%C A229084 +-+--+--+---+---+---+---+----+----+----+----+----+----+----+
%C A229084 |1|10|11|100|101|110|111|1000|1001|1010|1011|1100|1101|1110|...
%C A229084 +-+--+--+---+---+---+---+----+----+----+----+----+----+----+
%C A229084 This sequence:
%C A229084 +----+-+----+--+--+---+------+---+-----+-----+----+----+----+
%C A229084 | 110|1|1100|10|11|101|111000|100|11010|10111|1001|1011|1101|...
%C A229084 +----+-+----+--+--+---+------+---+-----+-----+----+----+----+
%C A229084 Numbers from this sequence written in base 10 (A229085):
%C A229084 +----+-+----+--+--+---+------+---+-----+-----+----+----+----+
%C A229084 |  6 |1| 12 | 2| 3| 5 |  56  | 4 |  26 |  23 |  9 |  11|  13|...
%C A229084 +----+-+----+--+--+---+------+---+-----+-----+----+----+----+
%H A229084 Paul Tek, <a href="/A229084/b229084.txt">Table of n, a(n) for n = 1..10000</a>
%Y A229084 Cf. A228595 (like sequence in base 10), A007088 (numbers written in base 2), A229085.
%K A229084 nonn,base
%O A229084 1,1
%A A229084 _Jaroslav Krizek_, Sep 13 2013