160109(2)

Ruby


9 × (10^(18n) - 1) / 19 の性質について(1)

 2, … , 9 倍すると大体数字がずれた状態になる。
例えば、
473684210526315789 × 1 = 473684210526315789

473684210526315789 × 2 = 947368421052631578

473684210526315789 × 3 = 1421052631578947367

473684210526315789 × 4 = 1894736842105263156

473684210526315789 × 5 = 2368421052631578945

473684210526315789 × 6 = 2842105263157894734

473684210526315789 × 7 = 3315789473684210523

473684210526315789 × 8 = 3789473684210526312

473684210526315789 × 9 = 4263157894736842101

473684210526315789473684210526315789 × 1 = 473684210526315789473684210526315789

473684210526315789473684210526315789 × 2 = 947368421052631578947368421052631578

473684210526315789473684210526315789 × 3 = 1421052631578947368421052631578947367

473684210526315789473684210526315789 × 4 = 1894736842105263157894736842105263156

473684210526315789473684210526315789 × 5 = 2368421052631578947368421052631578945

473684210526315789473684210526315789 × 6 = 2842105263157894736842105263157894734

473684210526315789473684210526315789 × 7 = 3315789473684210526315789473684210523

473684210526315789473684210526315789 × 8 = 3789473684210526315789473684210526312

473684210526315789473684210526315789 × 9 = 4263157894736842105263157894736842101

def f(n)
  (9 * (10 ** (18 * n) - 1)) / 19
end

n = 10
p ary = (0..n).map{|i| f(i)}
# それぞれj倍したもの
ary.each{|i| p (1..9).map{|j| i * j}}

出力結果
[0, 473684210526315789, 473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789]
[0, 0, 0, 0, 0, 0, 0, 0, 0]
[473684210526315789, 947368421052631578, 1421052631578947367, 1894736842105263156, 2368421052631578945, 2842105263157894734, 3315789473684210523, 3789473684210526312, 4263157894736842101]
[473684210526315789473684210526315789, 947368421052631578947368421052631578, 1421052631578947368421052631578947367, 1894736842105263157894736842105263156, 2368421052631578947368421052631578945, 2842105263157894736842105263157894734, 3315789473684210526315789473684210523, 3789473684210526315789473684210526312, 4263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842101]
[473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842101]