A328173 - OEIS

%I #30 Oct 06 2019 12:46:00

%S 4,5,6,9,10,11,20,22,30,33,44,55,57,66,77,99,100,111,159,171,200,222,

%T 300,333,444,555,666,704,889,999,1000,1111,1149,1578,1755,2000,2025,

%U 2222,2618,3000,3111,3333,6666,7777,9999,10000,11111,20000,22222,22568,22972,30000,30297,33333

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

%H Seiichi Manyama, <a href="/A328173/b328173.txt">Table of n, a(n) for n = 1..127</a>

%e    4^2 =   16,   1 +  6 =   7.

%e    5^2 =   25,   2 +  5 =   7.

%e    6^2 =   36,   3 +  6 =   9.

%e    9^2 =   81,   8 +  1 =   9.

%e   10^2 =  100,   1 +  0 =   1.

%e   11^2 =  121,   1 + 21 =  22.

%e   20^2 =  400,   4 +  0 =   4.

%e   22^2 =  484,   4 + 84 =  88.

%e   30^2 =  900,   9 +  0 =   9.

%e   33^2 = 1089,  10 + 89 =  99.

%e   44^2 = 1936,  19 + 36 =  55.

%e   55^2 = 3025,  30 + 25 =  55.

%e   57^2 = 3249, 324 +  9 = 333.

%e   66^2 = 4356,  43 + 56 =  99.

%e   77^2 = 5929,  59 + 29 =  88.

%e   99^2 = 9801,  98 +  1 =  99.

%o (Ruby)

%o def A(str)

%o   (0..str.size - 2).any?{|i| (str[0..i].to_i + str[i + 1..-1].to_i).to_s.split('').uniq.size == 1}

%o end

%o p (0..10 ** 4).select{|i| A((i * i).to_s)}

%Y Cf. A000290, A010785, A248353.

%K nonn,base

%O 1,1

%A _Seiichi Manyama_, Oct 06 2019