[seqfan] Resurrect A090566?

[David Wilson]

A082209 is defined as:

 

a(1) = 1, a(n+1) = smallest k with concat(a(n), k) square.

 

A090566 was deaded as an erroneous version of A082209. But I could argue
that A090566 was meant to be a different sequence, namely:

 

a(1) = 1, a(n+1) = smallest k > a(n) with concat(a(n), k) square.

 

Observe that A090566 in increasing and that concatenating adjacent elements
of A090566 gives square numbers. This supports my interpretation.

By this new definition, A090566 is still incorrect starting at a(5), perhaps
due to computation error. Corrected, I believe it begins

 

1,6,25,281,961,6201,59409,187600,730641,4429444,28600025,85336064

 

This sequence does not occur elsewhere in the OEIS, so I propose to
resurrect A090566 with this new definition (or create a new sequence if this
is unacceptable).

 

I computed the above elements using a brute force C++ program, but with the
appropriate power tools, e.g. Mma, and a little cleverness, I think this
sequence could be generated quite efficiently. Anyone up to verifying and
extending my values?