%I #12 Oct 02 2013 13:38:40

%S 1,1,5,7,31,43,138

%N Number of rational knots with n crossings with unknotting gap.

%D S. A. Bleiler, A note on unknotting number, Math. Proc. Camb. Phil. Soc. 96 (1984) 469-471.

%D D. Garity, Unknotting numbers are not realized in minimal projections for a class of rational knots. Proceedings of the "II Italian-Spanish Congress on General Topology and its Applications" (Trieste, 1999). Rend. Istit. Mat. Univ. Trieste 32 (2001), suppl. 2, 59-72 (2002).

%D Y. Nakanishi, Unknotting numbers and knot diagrams with the minimum crossings, Math. Sem. Notes Kobe Univ. 11 (1983) 257-258.

%H D. Garity, <a href="http://oregonstate.edu/~garityd/">Unknotting Numbers are not Realized in Minimal Projections for a Class of Rational Knots</a>

%H S. Jablan and R. Sazdanovic, <a href="http://www.mi.sanu.ac.rs/vismath/linknot/">LinKnot</a>

%e The first knot with unknotting gap is 10_8=514 (Nakanishi-Bleiler example).

%e For n=11 there is a knot 4142, etc.

%Y Cf. A090936.

%K nonn

%O 10,3

%A Slavik Jablan and Radmila Sazdanovic (jablans(AT)mi.sanu.ac.rs), Feb 26 2004; corrected Aug 29 2004