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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.
6

%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