Is there Meaning or Significance to the numbers 5, 21, and 31?

Most Aikido styles that use weapons have a 5, 8, 21, and 31 step kata. I can see the 8 as a form that faces the cardinal directions and I have read some interesting explanations from John Steven's books on that one. Are there any known reasons for using the other numbers?

Well realizing there is a 13 step kata as well the sequence becomes clearer

1 1 2 3 5 8 13 21 34

Obviously the 31 kata is miscounted (yes we all screw up counting in that one ) and should be 34

This makes it clear that the next one should be 55 steps. Fibonacci numbers ftw

i am waiting for the 42 which is really the answer

All kata I have seen or done are done equally in left and right hanmi, then all katas are even unless there is a moved to change hanmi in the middle of the kata.

dps

In Saito-shihan's Aikijo and Aikiken instructional videos he describes that the 13-count jo kata was a second jo kata that Kaiso [O-Sensei] taught him, but that the sole reason that it is only 13-count is because, in his words, "that is all I can remember."