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a(1) = 64; for n > 1 a(n) is the smallest square > a(n-1) with a(n-1) forming its final digits.
3

%I #6 Jun 12 2023 19:38:27

%S 64,1764,6041764,96126041764,8584885596126041764,

%T 1094573934406914368584885596126041764,

%U 164840278246153785356947805564195221094573934406914368584885596126041764

%N a(1) = 64; for n > 1 a(n) is the smallest square > a(n-1) with a(n-1) forming its final digits.

%C a(n) = A050636(n+1) for n >= 1.

%t nxt[n_]:=Module[{k=1},While[!IntegerQ[Sqrt[k*10^IntegerLength[n]+n]],k++];k*10^IntegerLength[n]+n]; NestList[nxt,64,6] (* _Harvey P. Dale_, Dec 14 2019 *)

%Y A050634, A050636, A065689, A065789, A065790.

%K base,nonn

%O 1,1

%A _Klaus Brockhaus_, Nov 19 2001