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A048422 Numbers k such that k^2 is formed from two subsquares that overlap in a single digit. 1

%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 1-digit 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, m-1], 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

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Last modified August 17 12:30 EDT 2022. Contains 356189 sequences. (Running on oeis4.)