%I #21 May 26 2019 14:23:56
%S 1,10,100,1001,10010,100101,1001101,10010110,101001101,1001011001,
%T 10010110010,100101100101,1001101001101,10010110010110,
%U 101001101001101,1001011001011001,10010110010110010,100101100101100101
%N Consider numbers m in the range 2^n <= m < 2^(n+1); the smallest A215244(m) in this range is k=A215245(n); a(n) = binary representation of m for the first time this k appears.
%C a(n) is an example, the first that is encountered, of a binary vector of length n that has the smallest number of factorizations as a product of palindromes.
%H Lars Blomberg, <a href="/A215254/b215254.txt">Table of n, a(n) for n = 0..26</a>
%e If the numbers are written under each other, there is a suggestion of a pattern (see A215255 for the most obvious pattern). It would be interesting to have more terms to see if the pattern continues.
%e 0 1 1
%e 1 10 10
%e 2 100 100
%e 3 1001 1001
%e 4 10010 10010
%e 5 100101 a
%e 6 1001101 b1
%e 7 10010110 a10
%e 8 101001101 10b1
%e 9 1001011001 a1001
%e 10 10010110010 a10010
%e 11 100101100101 aa
%e 12 1001101001101 bb1
%e 13 10010110010110 aa10
%e 14 101001101001101 10bb1
%e 15 1001011001011001 aa1001
%e 16 10010110010110010 aa10010
%e 17 100101100101100101 aaa
%e 18 1001101001101001101 bbb1
%e 19 10010110010110010110 aaa10
%e 20 101001101001101001101 10bbb1
%e 21 1001011001011001011001 aaa1001
%e 22 10010110010110010110010 aaa10010
%e 23 100101100101100101100101 aaaa
%e 24 1001101001101001101001101 bbbb1
%e 25 10010110010110010110010110 aaaa10
%e 26 101001101001101001101001101 10bbbb1
%e The rightmost column is obtained by substituting a=100101 and b=100110. A period of 6 is apparent. - _Lars Blomberg_, May 18 2019
%Y Cf. A215244, A215245, A215246, A215253, A215255.
%K nonn,base
%O 0,2
%A _N. J. A. Sloane_, Aug 14 2012
%E Example augmented by _Lars Blomberg_, May 18 2019