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.

1, 10, 100, 1001, 10010, 100101, 1001101, 10010110, 101001101, 1001011001, 10010110010, 100101100101, 1001101001101, 10010110010110, 101001101001101, 1001011001011001, 10010110010110010, 100101100101100101

Offset

0,2

Comments

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.

Links

Lars Blomberg, Table of n, a(n) for n = 0..26

Example

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.
   0  1                            1
   1  10                           10
   2  100                          100
   3  1001                         1001
   4  10010                        10010
   5  100101                       a
   6  1001101                      b1
   7  10010110                     a10
   8  101001101                    10b1
   9  1001011001                   a1001
  10  10010110010                  a10010
  11  100101100101                 aa
  12  1001101001101                bb1
  13  10010110010110               aa10
  14  101001101001101              10bb1
  15  1001011001011001             aa1001
  16  10010110010110010            aa10010
  17  100101100101100101           aaa
  18  1001101001101001101          bbb1
  19  10010110010110010110         aaa10
  20  101001101001101001101        10bbb1
  21  1001011001011001011001       aaa1001
  22  10010110010110010110010      aaa10010
  23  100101100101100101100101     aaaa
  24  1001101001101001101001101    bbbb1
  25  10010110010110010110010110   aaaa10
  26  101001101001101001101001101  10bbbb1
The rightmost column is obtained by substituting a=100101 and b=100110. A period of 6 is apparent. - Lars Blomberg, May 18 2019

Crossrefs

Cf. A215244, A215245, A215246, A215253, A215255.

Sequence in context: A351386 A102397 A132347 * A262863 A267156 A267524

Adjacent sequences: A215251 A215252 A215253 * A215255 A215256 A215257

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 14 2012

Extensions

Example augmented by Lars Blomberg, May 18 2019

Status

approved