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A309870 a(n) is the smallest number whose digits are 1's and 0's that cannot be written as a concatenation of any of the previous terms (not repeating any terms in the concatenation). a(0) = 0.

%I A309870 #30 Oct 13 2019 12:00:18
%S A309870 0,1,11,100,101,1111,10000,11001,11011,100010,100100,101000,101001,
%T A309870 101010,101101,110001,1000000,1000110,1001100,1010110,1100001,1110011,
%U A309870 1110111,10000010,10001000,10001110,10010100,10011100,10100000,10101110,10111010
%N A309870 a(n) is the smallest number whose digits are 1's and 0's that cannot be written as a concatenation of any of the previous terms (not repeating any terms in the concatenation). a(0) = 0.
%C A309870 For each term k, k||k is also a term, where || denotes the operation of concatenation.
%H A309870 Mason C. Hart, <a href="/A309870/b309870.txt">Table of n, a(n) for n = 0..499</a>
%H A309870 Mason C. Hart, <a href="/A309870/a309870.txt">Python program to calculate b-file</a>
%e A309870 1 cannot be written as a concatenation of 0, therefore a(1) is 1.
%e A309870 10 = 1||0 but 11 cannot be concatenated 11 = 1||1 because 1 can only be used once, therefore a(2) is 11.
%Y A309870 Subsequence of A007088 (binary numbers).
%K A309870 base,nonn
%O A309870 0,3
%A A309870 _Mason C. Hart_, Aug 20 2019