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.

0, 1, 11, 100, 101, 1111, 10000, 11001, 11011, 100010, 100100, 101000, 101001, 101010, 101101, 110001, 1000000, 1000110, 1001100, 1010110, 1100001, 1110011, 1110111, 10000010, 10001000, 10001110, 10010100, 10011100, 10100000, 10101110, 10111010

Offset

0,3

Comments

For each term k, k||k is also a term, where || denotes the operation of concatenation.

Links

Mason C. Hart, Table of n, a(n) for n = 0..499

Mason C. Hart, Python program to calculate b-file

Example

1 cannot be written as a concatenation of 0, therefore a(1) is 1.
10 = 1||0 but 11 cannot be concatenated 11 = 1||1 because 1 can only be used once, therefore a(2) is 11.

Crossrefs

Subsequence of A007088 (binary numbers).

Sequence in context: A261757 A280049 A066329 * A219896 A330898 A287739

Adjacent sequences: A309867 A309868 A309869 * A309871 A309872 A309873

Keyword

base,nonn

Author

Mason C. Hart, Aug 20 2019

Status

approved