[seqfan] Squares with even-positioned digits matching the original number

[David Radcliffe]

Hi all,

I recently came across sequence A326418, which is described as "Nonnegative
numbers k such that, in decimal representation, the subsequence of digits
of k^2 occupying an odd position is equal to the digits of k." I was
wondering about the analogous problem for even positions, but that sequence
is not in the OEIS.

I performed a search up to 10^16, and the only example I found was k =
9678692507732, excluding multiples of 10.

This is a term because k^2 = 93677088659227550879783824, and if we remove
every other digit from k^2, starting with the units digit, we get back to
9678692507732.

Are there other solutions? I am intrigued by this sequence because the
first term is so large, but I don't know enough terms to propose it for
inclusion in the OEIS.

- David