Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Jan 08 2019 19:11:42
%S 1,2,2,4,6,8,16,24,46,84,160,300,588,1136,2236,4388,8690
%N Number of (strongly) superprimitive binary sequences of length n.
%C A string x of length n is (weakly) quasiperiodic if there is a string w of length < n for which copies can be placed (possibly overlapping; possibly hanging off the left and right ends of x) that completely cover x. For example, x = 001101 is weakly quasiperiodic with quasiperiod w = 0110; three copies of w suffice to cover x. A string is (strongly) superprimitive if it is not weakly quasiperiodic.
%H A. Apostolico, M. Farach, and C. S. Iliopoulos, <a href="https://doi.org/10.1016/0020-0190(91)90056-N">Optimal superprimitivity testing for strings</a>, Info. Proc. Letters 39 (1991), 17-20.
%e a(6) = 16 because the 8 strings
%e 000001,
%e 000011,
%e 000101,
%e 000111,
%e 001011,
%e 001111,
%e 010111,
%e 011111
%e and their complements are strongly superprimitive.
%K nonn,more
%O 0,2
%A _Jeffrey Shallit_, Mar 13 2013