awesome-numbers.rb

class Fixnum
  def prime?
    bound = Math.sqrt(self).floor
    bound < 2 || (2..bound).all? { |i| self % i > 0 }
  end

  def palindrome?
    str = self.to_s
    len = str.length
    last = len - 1
    (0..(len/2-1)).all? { |i| str[i] == str[last-i] }
  end

  def awesome?(leet = true)
    return false  if leet && (!self.palindrome? || self.prime?)

    n = self
    factors = []
    while !n.prime?
      bound = Math.sqrt(n).floor
      x = (2..bound).find { |i| n % i == 0 }
      return false  if !x.palindrome?
      factors << x
      n = n / x
    end
    if n.palindrome?
      factors << n
      factors
    else
      false
    end
  end
end

(2..1_000_000).each do |n|
  #$stderr.puts(n)
  result = n.awesome?
  puts "% 7d => %s" % [n, result.inspect] if result
end

result.txt

      4 => [2, 2]
      6 => [2, 3]
      8 => [2, 2, 2]
      9 => [3, 3]
     22 => [2, 11]
     33 => [3, 11]
     44 => [2, 2, 11]
     55 => [5, 11]
     66 => [2, 3, 11]
     77 => [7, 11]
     88 => [2, 2, 2, 11]
     99 => [3, 3, 11]
    121 => [11, 11]
    202 => [2, 101]
    242 => [2, 11, 11]
    252 => [2, 2, 3, 3, 7]
    262 => [2, 131]
    303 => [3, 101]
    343 => [7, 7, 7]
    363 => [3, 11, 11]
    393 => [3, 131]
    404 => [2, 2, 101]
    484 => [2, 2, 11, 11]
    505 => [5, 101]
    525 => [3, 5, 5, 7]
    606 => [2, 3, 101]
    616 => [2, 2, 2, 7, 11]
    626 => [2, 313]
    686 => [2, 7, 7, 7]
    707 => [7, 101]
    808 => [2, 2, 2, 101]
    909 => [3, 3, 101]
    939 => [3, 313]
   1111 => [11, 101]
   1331 => [11, 11, 11]
   1441 => [11, 131]
   1661 => [11, 151]
   1991 => [11, 181]
   2112 => [2, 2, 2, 2, 2, 2, 3, 11]
   2222 => [2, 11, 101]
   2662 => [2, 11, 11, 11]
   2772 => [2, 2, 3, 3, 7, 11]
   2882 => [2, 11, 131]
   3333 => [3, 11, 101]
   3443 => [11, 313]
   3773 => [7, 7, 7, 11]
   3883 => [11, 353]
   3993 => [3, 11, 11, 11]
   4224 => [2, 2, 2, 2, 2, 2, 2, 3, 11]
   4444 => [2, 2, 11, 101]
   5445 => [3, 3, 5, 11, 11]
   5555 => [5, 11, 101]
   5775 => [3, 5, 5, 7, 11]
   6336 => [2, 2, 2, 2, 2, 2, 3, 3, 11]
   6666 => [2, 3, 11, 101]
   6776 => [2, 2, 2, 7, 11, 11]
   6886 => [2, 11, 313]
   7777 => [7, 11, 101]
   7997 => [11, 727]
   8448 => [2, 2, 2, 2, 2, 2, 2, 2, 3, 11]
   8888 => [2, 2, 2, 11, 101]
   9999 => [3, 3, 11, 101]
  10201 => [101, 101]
  12221 => [11, 11, 101]
  13231 => [101, 131]
  14641 => [11, 11, 11, 11]
  15251 => [101, 151]
  15851 => [11, 11, 131]
  18281 => [101, 181]
  19291 => [101, 191]
  20402 => [2, 101, 101]
  20602 => [2, 10301]
  22622 => [2, 11311]
  22822 => [2, 11411]
  23232 => [2, 2, 2, 2, 2, 2, 3, 11, 11]
  24442 => [2, 11, 11, 101]
  24842 => [2, 12421]
  25152 => [2, 2, 2, 2, 2, 2, 3, 131]
  25452 => [2, 2, 3, 3, 7, 101]
  26462 => [2, 101, 131]
  26662 => [2, 13331]
  28682 => [2, 14341]
  30603 => [3, 101, 101]
  30903 => [3, 10301]
  31613 => [101, 313]
  33933 => [3, 11311]
  34643 => [7, 7, 7, 101]
  35653 => [101, 353]
  36663 => [3, 11, 11, 101]
  37673 => [101, 373]
  37873 => [11, 11, 313]
  38683 => [101, 383]
  39693 => [3, 101, 131]
  39993 => [3, 13331]
  40804 => [2, 2, 101, 101]
  46464 => [2, 2, 2, 2, 2, 2, 2, 3, 11, 11]
  48384 => [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7]
  48884 => [2, 2, 11, 11, 101]
  52525 => [5, 5, 11, 191]
  59895 => [3, 3, 5, 11, 11, 11]
  60206 => [2, 30103]
  60406 => [2, 30203]
  60806 => [2, 30403]
  62026 => [2, 31013]
  64646 => [2, 32323]
  64846 => [2, 32423]
  65856 => [2, 2, 2, 2, 2, 2, 3, 7, 7, 7]
  67776 => [2, 2, 2, 2, 2, 2, 3, 353]
  69696 => [2, 2, 2, 2, 2, 2, 3, 3, 11, 11]
  82728 => [2, 2, 2, 3, 3, 3, 383]
  88788 => [2, 2, 3, 7, 7, 151]
  90309 => [3, 30103]
  90609 => [3, 30203]
  93039 => [3, 31013]
  96969 => [3, 32323]
 112211 => [11, 101, 101]
 113311 => [11, 10301]
 115511 => [11, 10501]
 116611 => [11, 10601]
 124421 => [11, 11311]
 125521 => [11, 11411]
 134431 => [11, 11, 11, 101]
 136631 => [11, 12421]
 139931 => [11, 12721]
 145541 => [11, 101, 131]
 146641 => [11, 13331]
 157751 => [11, 14341]
 167761 => [11, 101, 151]
 169961 => [11, 15451]
 176671 => [11, 16061]
 179971 => [11, 16361]
 199991 => [11, 18181]
 213312 => [2, 2, 2, 2, 2, 2, 3, 11, 101]
 224422 => [2, 11, 101, 101]
 226622 => [2, 11, 10301]
 248842 => [2, 11, 11311]
 255552 => [2, 2, 2, 2, 2, 2, 3, 11, 11, 11]
 268862 => [2, 11, 11, 11, 101]
 276672 => [2, 2, 2, 2, 2, 2, 3, 11, 131]
 279972 => [2, 2, 3, 3, 7, 11, 101]
 331133 => [11, 30103]
 332233 => [11, 30203]
 334433 => [11, 30403]
 336633 => [3, 11, 101, 101]
 337733 => [11, 30703]
 338833 => [11, 30803]
 339933 => [3, 11, 10301]
 341143 => [11, 31013]
 346643 => [11, 31513]
 347743 => [11, 101, 313]
 355553 => [11, 32323]
 356653 => [11, 32423]
 368863 => [11, 33533]
 379973 => [11, 34543]
 385583 => [11, 35053]
 386683 => [11, 35153]
 388883 => [11, 35353]
 398893 => [11, 36263]
 405504 => [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 11]
 426624 => [2, 2, 2, 2, 2, 2, 2, 3, 11, 101]
 448844 => [2, 2, 11, 101, 101]
 526625 => [5, 5, 5, 11, 383]
 549945 => [3, 3, 5, 11, 11, 101]
 577775 => [5, 5, 11, 11, 191]
 639936 => [2, 2, 2, 2, 2, 2, 3, 3, 11, 101]
 657756 => [2, 2, 3, 3, 11, 11, 151]
 662266 => [2, 11, 30103]
 664466 => [2, 11, 30203]
 668866 => [2, 11, 30403]
 682286 => [2, 11, 31013]
 772277 => [11, 70207]
 775577 => [11, 70507]
 776677 => [11, 70607]
 784487 => [11, 71317]
 794497 => [11, 72227]
 799997 => [11, 72727]
 993399 => [3, 11, 30103]
 996699 => [3, 11, 30203]
 997799 => [11, 90709]