0,2

Martin Fuller (martin_n_fuller(AT)btinternet.com), Algorithm and table of n, c(n) for n = 1..69. [I don't know if it has been proved that A006697(n) gives the maximal number of distinct substrings of a binary string of length n for 29 <= n <= 69. - N. J. A. Sloane (njas(AT)research.att.com), Jan 31 2008]

Table giving n, A006697(n) = (conjectural) maximal number of distinct substrings of a binary string of length n, a(n), c(n) = lexically first length-n binary string with A006697(n) distinct substrings.

n A006697(n) a(n) c(n)

0 1 1 null

1 2 2 0

2 4 2 01

3 6 6 001

4 9 8 0010

5 13 4 00110

6 17 18 000110

7 22 38 0001011

8 28 48 00010110

9 35 40 000101100

10 43 16 0001011100

11 51 80 00001011100

12 60 210 000010011101

13 70 402 0000100110111

14 81 644 00001001101110

15 93 852 000010011010111

16 106 928 0000100110101110

17 120 912 00001001101011100

18 135 704 000010011010111000

19 151 256 0000100110101111000

20 167 1344 00000100110101111000

21 184 3944 000001000110101111001

22 202 9276 0000010001100101111010

23 221 19448 00000100011001010111101

24 241 37090 000001000110010101111010

25 262 65602 0000010001100101001111011

26 284 107388 00000100011001010011101111

27 307 160760 000001000110010100111011110

28 331 220200 0000010001100101001110101111

For (conjectural?) further values see that Martin Fuller link.

Cf. A006697, A134466(n) = decimal value of c(n) interpreted as a binary number.

Sequence in context: A106168 A106166 A101343 this_sequence A092522 A116542 A142243

Adjacent sequences: A134454 A134455 A134456 this_sequence A134458 A134459 A134460

nonn

David W. Wilson (wilson.d(AT)anseri.com), Dec 17 2007