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A328173 Numbers k such that decimal expansion of k^2 can be split into two parts whose sum is a number with repeated digits.

%I A328173 #30 Oct 06 2019 12:46:00
%S A328173 4,5,6,9,10,11,20,22,30,33,44,55,57,66,77,99,100,111,159,171,200,222,
%T A328173 300,333,444,555,666,704,889,999,1000,1111,1149,1578,1755,2000,2025,
%U A328173 2222,2618,3000,3111,3333,6666,7777,9999,10000,11111,20000,22222,22568,22972,30000,30297,33333
%N A328173 Numbers k such that decimal expansion of k^2 can be split into two parts whose sum is a number with repeated digits.
%H A328173 Seiichi Manyama, <a href="/A328173/b328173.txt">Table of n, a(n) for n = 1..127</a>
%e A328173    4^2 =   16,   1 +  6 =   7.
%e A328173    5^2 =   25,   2 +  5 =   7.
%e A328173    6^2 =   36,   3 +  6 =   9.
%e A328173    9^2 =   81,   8 +  1 =   9.
%e A328173   10^2 =  100,   1 +  0 =   1.
%e A328173   11^2 =  121,   1 + 21 =  22.
%e A328173   20^2 =  400,   4 +  0 =   4.
%e A328173   22^2 =  484,   4 + 84 =  88.
%e A328173   30^2 =  900,   9 +  0 =   9.
%e A328173   33^2 = 1089,  10 + 89 =  99.
%e A328173   44^2 = 1936,  19 + 36 =  55.
%e A328173   55^2 = 3025,  30 + 25 =  55.
%e A328173   57^2 = 3249, 324 +  9 = 333.
%e A328173   66^2 = 4356,  43 + 56 =  99.
%e A328173   77^2 = 5929,  59 + 29 =  88.
%e A328173   99^2 = 9801,  98 +  1 =  99.
%o A328173 (Ruby)
%o A328173 def A(str)
%o A328173   (0..str.size - 2).any?{|i| (str[0..i].to_i + str[i + 1..-1].to_i).to_s.split('').uniq.size == 1}
%o A328173 end
%o A328173 p (0..10 ** 4).select{|i| A((i * i).to_s)}
%Y A328173 Cf. A000290, A010785, A248353.
%K A328173 nonn,base
%O A328173 1,1
%A A328173 _Seiichi Manyama_, Oct 06 2019