When the heapsort worst case occurs?
Please check the paper@arXiv2015: A Complete Worst-Case Analysis of Heapsort by M. A. Suchenek.

This paper gives a rather involved lower bound; see Abstract and Theorem 12.2 on page 94.

To the specific question,


  Example of a 500-node worst-case array for Heapsort, created by my
  Java program, is included in Appendix A.3 page 110.