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%I #9 Oct 13 2017 03:30:59
%S 8,41,209,764,5225,8441,9344,63761,82201,477264,3191044,4038489,
%T 34656049,61233321,271005625,3465072801,36565416324,83511106624,
%U 222222321476,425286636356,2743260628100,9534841632400,33984728488004,128198574830929,741089622057984,5579432351776489
%N a(1) = 8, a(n) = smallest number > a(n-1) such that the concatenation of a(n-1) and a(n) is a square.
%e a(3) is 209 since it is the least number greater than a(2)=41 which concatenated with 41 forms a perfect square, i.e., 41209 = 203^2.
%t f[n_] := Block[{x = n, d = 1 + Floor@ Log10@ n}, q = (Floor@ Sqrt[(10^d + 1) x] + 1)^2; If[q < (10^d) (x + 1), Mod[q, 10^d], Mod[(Floor@ Sqrt[(10^d)(10x + 1) - 1] + 1)^2, 10^(d + 1)] ]]; NestList[f, 8, 25] (* after the algorithm of _David W. Wilson_ in A090566 *)
%Y Cf. A090566, A265147, A265148, A265150, A265151, A265152, A265153, A265154, A265155.
%K nonn,base
%O 1,1
%A _Robert G. Wilson v_, Dec 02 2015