%I
%S 57,285,475,604,1442,2225,6293,6645,9175,9607,10815,16349,18493,25375,
%T 34825,38025,41225,48035,54075,54758,56605,60125,92971,98075,104956,
%U 106885,162225,196096,264904,392125,534425,572375,597675,635625,684475
%N Numbers k such that k^2 is formed from two subsquares that overlap in a single digit.
%C Subsquares with leading and/or trailing zeros not included. Subsquares are at least 2 digits long.
%e 57 is a term because 57^2 = 3249 in which we see 324 = 18^2 and 49 = 7^2 overlapping in a single digit, namely the digit 4.
%e 162225 is a term:
%e 162225^2 = 26316950625
%e 513^2 = 263169
%e 975^2 = 950625
%e ^
%e 
%e 1digit overlap
%t qQ[w_] := w[[1]] > 0 && w[[1]] > 0 && IntegerQ@ Sqrt@ FromDigits[w]; ok[n_] := n>9 && Mod[n, 10] > 0 && Block[{d = IntegerDigits[ n^2], m}, m = Length[d]; AnyTrue[ Range[2, m1], qQ[ Take[d, #]] && qQ[Take[d, {#, m}]] &]]; Select[Range[10^5], ok] (* _Giovanni Resta_, Oct 14 2019 *)
%Y Cf. A000290, A048421.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Apr 15 1999
