Iterating A066136

[Jonathan Post]

A066136 Primes are replaced by their local sequence number in
A000040<http://www.research.att.com/~njas/sequences/A000040>,
while composites are replaced by their sequence number in
A002808<http://www.research.att.com/~njas/sequences/A002808>;
(a kind of eigen- or home-indexing).

This function a(n), which is a permutation of 0, 1, 1, 2, 2, 3, 3, ..., n,
n, ...
may be iterated, if some formal notation is used for "undefined" -- such as
a(0) = -1.

a(a(n)) begins: -1,
0,1,0,2,1,1,2,1,2,1,3,3,2,2,4,3,4,4,5,3,5,6,6,4,7,8,9,7,10,...

One can make an infinite array whose kth row (starting k=1) is the kth
iteration of a(n).

1 | 0, 1, 2, 1, 3, 2, 4, 3, 4, 5, 5, 6, 6, 7, 8, 9, 7, 10, ...
2 | -1, 0,1,0,2,1,1,2,1,2,1,3,3,2,2,4,3,4,4,5,3,5,6,6,4,7,8,9,7,10,...
3 | -1, -1, 0, -1, 1, 0, 0, 1, 0, 2, 2, 1, 1, 1, 2, 1, 1, 3, ...
4 | -1, -1, -1, -1, 0, -1, -1, 0, -1, 1, 1, 0, 0, 0, 1, 0, 0, 2, ...
etcetera.

One may see that it takes longer and longer for each successive row to reach
its first value greater than 1. Other features seem interesting to me, but I
want to know if anyone else cares before I pursue it.  I'm tempted to think
that it is not arbitrary, especially as A066136 has "eigen" in its
definition, by analogy (not as a proper keyword).
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