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

1,1

Links

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

Example

   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.

Prog

(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)}

Crossrefs

Cf. A000290, A010785, A248353.

Sequence in context: A008854 A062726 A159629 * A223138 A287676 A082812

Adjacent sequences: A328170 A328171 A328172 * A328174 A328175 A328176

Keyword

nonn,base

Author

Seiichi Manyama, Oct 06 2019

Status

approved