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%I #23 Mar 30 2017 23:38:29
%S 1,2,3,4,5,6,7,8,9,10,11,12,20,22,23,24,25,26,27,28,29,30,13,32,33,34,
%T 35,36,37,38,39,40,14,15,16,42,43,44,45,46,47,48,49,50,17,18,19,21,52,
%U 53,54,55,56,57,58,59,60,62,63,64,65,66,67,68,69,70,72
%N A self-describing sequence: the zeros and ones in the decimal representation of the sequence correspond to the binary representation of the sequence.
%C The sequence is always extended with the smallest integer not yet present and not leading to a contradiction.
%C Numbers with neither 0 nor 1 in their decimal representation appear in increasing order.
%C Comments from _N. J. A. Sloane_, Nov 10 2016: (Start)
%C Here is another way to state the condition that the sequence must satisfy.
%C For each n, let D denote the concatenation of the first n terms in base 10, and let B denote the concatenation of the first n terms in base 2. Let D' be obtained from D by deleting all digits except 0 and 1.
%C Then D' must be a prefix of B.
%C In the examples below, D' appears in parentheses.
%C A278030 shows indices where the sequence changes from on or below the diagonal (a(n)<=n) to above the diagonal (a(n)>n), or vice versa. (End)
%H Rémy Sigrist, <a href="/A277861/b277861.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A277861/a277861.pl.txt">PERL program for A277861</a>
%e When computing the sequence, we must check that for any n > 0, the zeros and ones among the decimal representation of the first n terms match the beginning of the binary representation of these terms.
%e The following table depicts the first terms, alongside their binary representation, and the matching zeros and ones among their decimal representation (in parentheses):
%e n a(n) a(n) in binary First n terms in binary
%e -- ---- -------------- -----------------------
%e 1 1 1 (1)
%e 2 2 10 (1)10
%e 3 3 11 (1)1011
%e 4 4 100 (1)1011100
%e 5 5 101 (1)1011100101
%e 6 6 110 (1)1011100101110
%e 7 7 111 (1)1011100101110111
%e 8 8 1000 (1)10111001011101111000
%e 9 9 1001 (1)101110010111011110001001
%e 10 10 1010 (110)11100101110111100010011010
%e 11 11 1011 (11011)1001011101111000100110101011
%e 12 12 1100 (110111)0010111011110001001101010111100
%e 13 20 10100 (1101110)01011101111000100110101011110010100
%Y Cf. A007088, A278030.
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Nov 02 2016
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