A175808 - OEIS

%I #13 Oct 09 2021 07:00:48

%S 1,2,3,4,6,6,7,8,11,11,13,13,14,14,15,16,20,20,23,23,25,25,28,28,28,

%T 28,29,29,30,30,31,32,37,37,41,41,44,44,48,48,50,50,52,52,55,55,59,59,

%U 59,59,59,59,59,59,60,60,60,60,61,61,62,62,63,64

%N n-th term is the length of a shortest common superstring of the binary representations of all natural numbers from 1 to n.

%C If a(n) = 2^m, then we know that the lexicographically largest superstring coincides with the lexicographically largest de Bruijn sequence, B(2,m) (A166316(m)). - _Thomas Scheuerle_, Oct 09 2021

%F It appears that a(2^n-1) = 2^n-1 and a(2^n) = 2^n. - _Thomas Scheuerle_, Oct 09 2021

%e a(5)=6 because 6 is the length of 110100 or 101100, which are the 2 possible shortest common superstrings of 1,10,11,100,101.

%Y Cf. A175809 (number of shortest common superstrings).

%Y Cf. A056744 (least decimal values of shortest common superstrings).

%Y Cf. A166316, A016031.

%K nonn,base

%O 1,2

%A _Vladimir Reshetnikov_, Sep 08 2010

%E a(23)-a(64) from _Thomas Scheuerle_, Oct 09 2021