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

4, 5, 6, 9, 10, 11, 20, 22, 30, 33, 44, 55, 57, 66, 77, 99, 100, 111, 159, 171, 200, 222, 300, 333, 444, 555, 666, 704, 889, 999, 1000, 1111, 1149, 1578, 1755, 2000, 2025, 2222, 2618, 3000, 3111, 3333, 6666, 7777, 9999, 10000, 11111, 20000, 22222, 22568, 22972, 30000, 30297, 33333

Offset: 1

Author

Seiichi Manyama, Oct 06 2019

Keywords

• nonn
• base

Examples

			   4^2 =   16,   1 +  6 =   7.
   5^2 =   25,   2 +  5 =   7.
   6^2 =   36,   3 +  6 =   9.
   9^2 =   81,   8 +  1 =   9.
  10^2 =  100,   1 +  0 =   1.
  11^2 =  121,   1 + 21 =  22.
  20^2 =  400,   4 +  0 =   4.
  22^2 =  484,   4 + 84 =  88.
  30^2 =  900,   9 +  0 =   9.
  33^2 = 1089,  10 + 89 =  99.
  44^2 = 1936,  19 + 36 =  55.
  55^2 = 3025,  30 + 25 =  55.
  57^2 = 3249, 324 +  9 = 333.
  66^2 = 4356,  43 + 56 =  99.
  77^2 = 5929,  59 + 29 =  88.
  99^2 = 9801,  98 +  1 =  99.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..127

Crossrefs

Cf. A000290, A010785, A248353.

Programs

Ruby

def A(str)
  (0..str.size - 2).any?{|i| (str[0..i].to_i + str[i + 1..-1].to_i).to_s.split('').uniq.size == 1}
end
p (0..10 ** 4).select{|i| A((i * i).to_s)}