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A346678 Positive numbers whose squares end in exactly two identical digits.

%I A346678 #35 Aug 05 2021 17:08:33
%S A346678 10,12,20,30,40,50,60,62,70,80,88,90,110,112,120,130,138,140,150,160,
%T A346678 162,170,180,188,190,210,212,220,230,238,240,250,260,262,270,280,288,
%U A346678 290,310,312,320,330,338,340,350,360,362,370,380,388,390,410,412,420,430,438,440,450,460
%N A346678 Positive numbers whose squares end in exactly two identical digits.
%C A346678 When a square ends in exactly two identical digits, these digits are necessarily 00 or 44, so all terms are even.
%C A346678 The numbers are of the form: 10*floor((10*k-1)/9), k > 0, or, 50*floor((10*k-1)/9) +- 38, k > 0.
%C A346678 Equivalently: m is in the sequence iff either (m == 0 (mod 10) and m <> 0 (mod 100)) or (m == +- 38 (mod 50) and m <> +- 38 (mod 500)).
%H A346678 <a href="/index/Rec#order_64">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F A346678 a(n+63) = a(n) + 500.
%e A346678 12 is in the sequence because 12^2 = 144 ends in two 4's.
%e A346678 20 is in the sequence because 20^2 = 400 ends in two 0's.
%e A346678 38 is not in the sequence because 38^2 = 1444 ends in three 4's.
%t A346678 Select[Range[10, 460], (d = IntegerDigits[#^2])[[-1]] == d[[-2]] != d[[-3]] &] (* _Amiram Eldar_, Jul 29 2021 *)
%o A346678 (Python)
%o A346678 def ok(n): s = str(n*n); return len(s) > 2 and s[-1] == s[-2] != s[-3]
%o A346678 print(list(filter(ok, range(461)))) # _Michael S. Branicky_, Jul 29 2021
%Y A346678 Equals A186438 \ A186439.
%Y A346678 Supersequence of A346774.
%K A346678 nonn,base,easy
%O A346678 1,1
%A A346678 _Bernard Schott_, Jul 29 2021