cp's OEIS Frontend

A215254 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.

%I A215254 #21 May 26 2019 14:23:56
%S A215254 1,10,100,1001,10010,100101,1001101,10010110,101001101,1001011001,
%T A215254 10010110010,100101100101,1001101001101,10010110010110,
%U A215254 101001101001101,1001011001011001,10010110010110010,100101100101100101
%N A215254 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 A215254 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 A215254 Lars Blomberg, <a href="/A215254/b215254.txt">Table of n, a(n) for n = 0..26</a>
%e A215254 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 A215254    0  1                            1
%e A215254    1  10                           10
%e A215254    2  100                          100
%e A215254    3  1001                         1001
%e A215254    4  10010                        10010
%e A215254    5  100101                       a
%e A215254    6  1001101                      b1
%e A215254    7  10010110                     a10
%e A215254    8  101001101                    10b1
%e A215254    9  1001011001                   a1001
%e A215254   10  10010110010                  a10010
%e A215254   11  100101100101                 aa
%e A215254   12  1001101001101                bb1
%e A215254   13  10010110010110               aa10
%e A215254   14  101001101001101              10bb1
%e A215254   15  1001011001011001             aa1001
%e A215254   16  10010110010110010            aa10010
%e A215254   17  100101100101100101           aaa
%e A215254   18  1001101001101001101          bbb1
%e A215254   19  10010110010110010110         aaa10
%e A215254   20  101001101001101001101        10bbb1
%e A215254   21  1001011001011001011001       aaa1001
%e A215254   22  10010110010110010110010      aaa10010
%e A215254   23  100101100101100101100101     aaaa
%e A215254   24  1001101001101001101001101    bbbb1
%e A215254   25  10010110010110010110010110   aaaa10
%e A215254   26  101001101001101001101001101  10bbbb1
%e A215254 The rightmost column is obtained by substituting a=100101 and b=100110. A period of 6 is apparent. - _Lars Blomberg_, May 18 2019
%Y A215254 Cf. A215244, A215245, A215246, A215253, A215255.
%K A215254 nonn,base
%O A215254 0,2
%A A215254 _N. J. A. Sloane_, Aug 14 2012
%E A215254 Example augmented by _Lars Blomberg_, May 18 2019