gistfile1.rb

#!/usr/bin/ruby

i = 0
founds = 0
begin
  i += 1
  sq = i ** 2
  digits = Math.log10(sq).to_i + 1
  next if digits % 2 == 1
  m = 10**(digits/2)
  if (sq/m - sq%m).abs == 1
    founds += 1
    puts "%d: %d (%d^2)" % [founds, sq, i]
  end
end while founds < 21