160419

Ruby


99…9 の累乗

http://www004.upp.so-net.ne.jp/s_honma/relax/integer13.html
を見て、99…9 の累乗の各桁の数字の和を計算してみた。

5乗までは規則正しい。

(1..6).each{|i|
  (0..15).each{|j|
    m = ('9' * j).to_i ** i
    p [m.to_s.split('').map(&:to_i).inject(:+), m]
  }
  p ''
}

出力結果
[0, 0]
[9, 9]
[18, 99]
[27, 999]
[36, 9999]
[45, 99999]
[54, 999999]
[63, 9999999]
[72, 99999999]
[81, 999999999]
[90, 9999999999]
[99, 99999999999]
[108, 999999999999]
[117, 9999999999999]
[126, 99999999999999]
[135, 999999999999999]
""
[0, 0]
[9, 81]
[18, 9801]
[27, 998001]
[36, 99980001]
[45, 9999800001]
[54, 999998000001]
[63, 99999980000001]
[72, 9999999800000001]
[81, 999999998000000001]
[90, 99999999980000000001]
[99, 9999999999800000000001]
[108, 999999999998000000000001]
[117, 99999999999980000000000001]
[126, 9999999999999800000000000001]
[135, 999999999999998000000000000001]
""
[0, 0]
[18, 729]
[36, 970299]
[54, 997002999]
[72, 999700029999]
[90, 999970000299999]
[108, 999997000002999999]
[126, 999999700000029999999]
[144, 999999970000000299999999]
[162, 999999997000000002999999999]
[180, 999999999700000000029999999999]
[198, 999999999970000000000299999999999]
[216, 999999999997000000000002999999999999]
[234, 999999999999700000000000029999999999999]
[252, 999999999999970000000000000299999999999999]
[270, 999999999999997000000000000002999999999999999]
""
[0, 0]
[18, 6561]
[36, 96059601]
[54, 996005996001]
[72, 9996000599960001]
[90, 99996000059999600001]
[108, 999996000005999996000001]
[126, 9999996000000599999960000001]
[144, 99999996000000059999999600000001]
[162, 999999996000000005999999996000000001]
[180, 9999999996000000000599999999960000000001]
[198, 99999999996000000000059999999999600000000001]
[216, 999999999996000000000005999999999996000000000001]
[234, 9999999999996000000000000599999999999960000000000001]
[252, 99999999999996000000000000059999999999999600000000000001]
[270, 999999999999996000000000000005999999999999996000000000000001]
""
[0, 0]
[27, 59049]
[54, 9509900499]
[81, 995009990004999]
[108, 99950009999000049999]
[135, 9999500009999900000499999]
[162, 999995000009999990000004999999]
[189, 99999950000009999999000000049999999]
[216, 9999999500000009999999900000000499999999]
[243, 999999995000000009999999990000000004999999999]
[270, 99999999950000000009999999999000000000049999999999]
[297, 9999999999500000000009999999999900000000000499999999999]
[324, 999999999995000000000009999999999990000000000004999999999999]
[351, 99999999999950000000000009999999999999000000000000049999999999999]
[378, 9999999999999500000000000009999999999999900000000000000499999999999999]
[405, 999999999999995000000000000009999999999999990000000000000004999999999999999]
""
[0, 0]
[18, 531441]
[45, 941480149401]
[72, 994014980014994001]
[99, 999400149980001499940001]
[126, 999940001499980000149999400001]
[153, 999994000014999980000014999994000001]
[180, 999999400000149999980000001499999940000001]
[207, 999999940000001499999980000000149999999400000001]
[234, 999999994000000014999999980000000014999999994000000001]
[261, 999999999400000000149999999980000000001499999999940000000001]
[288, 999999999940000000001499999999980000000000149999999999400000000001]
[315, 999999999994000000000014999999999980000000000014999999999994000000000001]
[342, 999999999999400000000000149999999999980000000000001499999999999940000000000001]
[369, 999999999999940000000000001499999999999980000000000000149999999999999400000000000001]
[396, 999999999999994000000000000014999999999999980000000000000014999999999999994000000000000001]
""