A216214 Number of (strongly) superprimitive binary sequences of length n.

1, 2, 2, 4, 6, 8, 16, 24, 46, 84, 160, 300, 588, 1136, 2236, 4388, 8690

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..16.

A. Apostolico, M. Farach, and C. S. Iliopoulos, Optimal superprimitivity testing for strings, Info. Proc. Letters 39 (1991), 17-20.

Example

a(6) = 16 because the 8 strings
000001,
000011,
000101,
000111,
001011,
001111,
010111,
011111
and their complements are strongly superprimitive.

Crossrefs

Sequence in context: A329137 A239851 A153958 * A269298 A153964 A001010

Adjacent sequences: A216211 A216212 A216213 * A216215 A216216 A216217

Keyword

nonn,more

Author

Jeffrey Shallit, Mar 13 2013

Status

approved