160109(3)

Ruby


9 × (10^(18n) - 1) / 19 の性質について(2)

k × (10^(18n) - m) / 19 で都合のよさそうなものを選んでみた。
例えば、
52631578947368421 × 1 =　52631578947368421

52631578947368421 × 2 =　105263157894736842
52631578947368421 × 3 =　157894736842105263
52631578947368421 × 4 =　210526315789473684
52631578947368421 × 5 =　263157894736842105
52631578947368421 × 6 =　315789473684210526
52631578947368421 × 7 =　368421052631578947
52631578947368421 × 8 =　421052631578947368
52631578947368421 × 9 =　473684210526315789

def f(k, n)
  m = (k * 10 ** (18 * n)) % 19
  return (k * 10 ** (18 * n) - m) / 19
end

n = 6
p ary = (0..n).inject([]){|s, i| s + (1..9).map{|k| f(k, i)}}.uniq!.sort
# 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, 52631578947368421, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789, 52631578947368421052631578947368421, 105263157894736842105263157894736842, 157894736842105263157894736842105263, 210526315789473684210526315789473684, 263157894736842105263157894736842105, 315789473684210526315789473684210526, 368421052631578947368421052631578947, 421052631578947368421052631578947368, 473684210526315789473684210526315789, 52631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789, 52631578947368421052631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789473684210526315789, 52631578947368421052631578947368421052631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789, 52631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789]
[0, 0, 0, 0, 0, 0, 0, 0, 0]
[52631578947368421, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789]
[105263157894736842, 210526315789473684, 315789473684210526, 421052631578947368, 526315789473684210, 631578947368421052, 736842105263157894, 842105263157894736, 947368421052631578]
[157894736842105263, 315789473684210526, 473684210526315789, 631578947368421052, 789473684210526315, 947368421052631578, 1105263157894736841, 1263157894736842104, 1421052631578947367]
[210526315789473684, 421052631578947368, 631578947368421052, 842105263157894736, 1052631578947368420, 1263157894736842104, 1473684210526315788, 1684210526315789472, 1894736842105263156]
[263157894736842105, 526315789473684210, 789473684210526315, 1052631578947368420, 1315789473684210525, 1578947368421052630, 1842105263157894735, 2105263157894736840, 2368421052631578945]
[315789473684210526, 631578947368421052, 947368421052631578, 1263157894736842104, 1578947368421052630, 1894736842105263156, 2210526315789473682, 2526315789473684208, 2842105263157894734]
[368421052631578947, 736842105263157894, 1105263157894736841, 1473684210526315788, 1842105263157894735, 2210526315789473682, 2578947368421052629, 2947368421052631576, 3315789473684210523]
[421052631578947368, 842105263157894736, 1263157894736842104, 1684210526315789472, 2105263157894736840, 2526315789473684208, 2947368421052631576, 3368421052631578944, 3789473684210526312]
[473684210526315789, 947368421052631578, 1421052631578947367, 1894736842105263156, 2368421052631578945, 2842105263157894734, 3315789473684210523, 3789473684210526312, 4263157894736842101]
[52631578947368421052631578947368421, 105263157894736842105263157894736842, 157894736842105263157894736842105263, 210526315789473684210526315789473684, 263157894736842105263157894736842105, 315789473684210526315789473684210526, 368421052631578947368421052631578947, 421052631578947368421052631578947368, 473684210526315789473684210526315789]
[105263157894736842105263157894736842, 210526315789473684210526315789473684, 315789473684210526315789473684210526, 421052631578947368421052631578947368, 526315789473684210526315789473684210, 631578947368421052631578947368421052, 736842105263157894736842105263157894, 842105263157894736842105263157894736, 947368421052631578947368421052631578]
[157894736842105263157894736842105263, 315789473684210526315789473684210526, 473684210526315789473684210526315789, 631578947368421052631578947368421052, 789473684210526315789473684210526315, 947368421052631578947368421052631578, 1105263157894736842105263157894736841, 1263157894736842105263157894736842104, 1421052631578947368421052631578947367]
[210526315789473684210526315789473684, 421052631578947368421052631578947368, 631578947368421052631578947368421052, 842105263157894736842105263157894736, 1052631578947368421052631578947368420, 1263157894736842105263157894736842104, 1473684210526315789473684210526315788, 1684210526315789473684210526315789472, 1894736842105263157894736842105263156]
[263157894736842105263157894736842105, 526315789473684210526315789473684210, 789473684210526315789473684210526315, 1052631578947368421052631578947368420, 1315789473684210526315789473684210525, 1578947368421052631578947368421052630, 1842105263157894736842105263157894735, 2105263157894736842105263157894736840, 2368421052631578947368421052631578945]
[315789473684210526315789473684210526, 631578947368421052631578947368421052, 947368421052631578947368421052631578, 1263157894736842105263157894736842104, 1578947368421052631578947368421052630, 1894736842105263157894736842105263156, 2210526315789473684210526315789473682, 2526315789473684210526315789473684208, 2842105263157894736842105263157894734]
[368421052631578947368421052631578947, 736842105263157894736842105263157894, 1105263157894736842105263157894736841, 1473684210526315789473684210526315788, 1842105263157894736842105263157894735, 2210526315789473684210526315789473682, 2578947368421052631578947368421052629, 2947368421052631578947368421052631576, 3315789473684210526315789473684210523]
[421052631578947368421052631578947368, 842105263157894736842105263157894736, 1263157894736842105263157894736842104, 1684210526315789473684210526315789472, 2105263157894736842105263157894736840, 2526315789473684210526315789473684208, 2947368421052631578947368421052631576, 3368421052631578947368421052631578944, 3789473684210526315789473684210526312]
[473684210526315789473684210526315789, 947368421052631578947368421052631578, 1421052631578947368421052631578947367, 1894736842105263157894736842105263156, 2368421052631578947368421052631578945, 2842105263157894736842105263157894734, 3315789473684210526315789473684210523, 3789473684210526315789473684210526312, 4263157894736842105263157894736842101]
[52631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789]
[105263157894736842105263157894736842105263157894736842, 210526315789473684210526315789473684210526315789473684, 315789473684210526315789473684210526315789473684210526, 421052631578947368421052631578947368421052631578947368, 526315789473684210526315789473684210526315789473684210, 631578947368421052631578947368421052631578947368421052, 736842105263157894736842105263157894736842105263157894, 842105263157894736842105263157894736842105263157894736, 947368421052631578947368421052631578947368421052631578]
[157894736842105263157894736842105263157894736842105263, 315789473684210526315789473684210526315789473684210526, 473684210526315789473684210526315789473684210526315789, 631578947368421052631578947368421052631578947368421052, 789473684210526315789473684210526315789473684210526315, 947368421052631578947368421052631578947368421052631578, 1105263157894736842105263157894736842105263157894736841, 1263157894736842105263157894736842105263157894736842104, 1421052631578947368421052631578947368421052631578947367]
[210526315789473684210526315789473684210526315789473684, 421052631578947368421052631578947368421052631578947368, 631578947368421052631578947368421052631578947368421052, 842105263157894736842105263157894736842105263157894736, 1052631578947368421052631578947368421052631578947368420, 1263157894736842105263157894736842105263157894736842104, 1473684210526315789473684210526315789473684210526315788, 1684210526315789473684210526315789473684210526315789472, 1894736842105263157894736842105263157894736842105263156]
[263157894736842105263157894736842105263157894736842105, 526315789473684210526315789473684210526315789473684210, 789473684210526315789473684210526315789473684210526315, 1052631578947368421052631578947368421052631578947368420, 1315789473684210526315789473684210526315789473684210525, 1578947368421052631578947368421052631578947368421052630, 1842105263157894736842105263157894736842105263157894735, 2105263157894736842105263157894736842105263157894736840, 2368421052631578947368421052631578947368421052631578945]
[315789473684210526315789473684210526315789473684210526, 631578947368421052631578947368421052631578947368421052, 947368421052631578947368421052631578947368421052631578, 1263157894736842105263157894736842105263157894736842104, 1578947368421052631578947368421052631578947368421052630, 1894736842105263157894736842105263157894736842105263156, 2210526315789473684210526315789473684210526315789473682, 2526315789473684210526315789473684210526315789473684208, 2842105263157894736842105263157894736842105263157894734]
[368421052631578947368421052631578947368421052631578947, 736842105263157894736842105263157894736842105263157894, 1105263157894736842105263157894736842105263157894736841, 1473684210526315789473684210526315789473684210526315788, 1842105263157894736842105263157894736842105263157894735, 2210526315789473684210526315789473684210526315789473682, 2578947368421052631578947368421052631578947368421052629, 2947368421052631578947368421052631578947368421052631576, 3315789473684210526315789473684210526315789473684210523]
[421052631578947368421052631578947368421052631578947368, 842105263157894736842105263157894736842105263157894736, 1263157894736842105263157894736842105263157894736842104, 1684210526315789473684210526315789473684210526315789472, 2105263157894736842105263157894736842105263157894736840, 2526315789473684210526315789473684210526315789473684208, 2947368421052631578947368421052631578947368421052631576, 3368421052631578947368421052631578947368421052631578944, 3789473684210526315789473684210526315789473684210526312]
[473684210526315789473684210526315789473684210526315789, 947368421052631578947368421052631578947368421052631578, 1421052631578947368421052631578947368421052631578947367, 1894736842105263157894736842105263157894736842105263156, 2368421052631578947368421052631578947368421052631578945, 2842105263157894736842105263157894736842105263157894734, 3315789473684210526315789473684210526315789473684210523, 3789473684210526315789473684210526315789473684210526312, 4263157894736842105263157894736842105263157894736842101]
[52631578947368421052631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789473684210526315789]
[105263157894736842105263157894736842105263157894736842105263157894736842, 210526315789473684210526315789473684210526315789473684210526315789473684, 315789473684210526315789473684210526315789473684210526315789473684210526, 421052631578947368421052631578947368421052631578947368421052631578947368, 526315789473684210526315789473684210526315789473684210526315789473684210, 631578947368421052631578947368421052631578947368421052631578947368421052, 736842105263157894736842105263157894736842105263157894736842105263157894, 842105263157894736842105263157894736842105263157894736842105263157894736, 947368421052631578947368421052631578947368421052631578947368421052631578]
[157894736842105263157894736842105263157894736842105263157894736842105263, 315789473684210526315789473684210526315789473684210526315789473684210526, 473684210526315789473684210526315789473684210526315789473684210526315789, 631578947368421052631578947368421052631578947368421052631578947368421052, 789473684210526315789473684210526315789473684210526315789473684210526315, 947368421052631578947368421052631578947368421052631578947368421052631578, 1105263157894736842105263157894736842105263157894736842105263157894736841, 1263157894736842105263157894736842105263157894736842105263157894736842104, 1421052631578947368421052631578947368421052631578947368421052631578947367]
[210526315789473684210526315789473684210526315789473684210526315789473684, 421052631578947368421052631578947368421052631578947368421052631578947368, 631578947368421052631578947368421052631578947368421052631578947368421052, 842105263157894736842105263157894736842105263157894736842105263157894736, 1052631578947368421052631578947368421052631578947368421052631578947368420, 1263157894736842105263157894736842105263157894736842105263157894736842104, 1473684210526315789473684210526315789473684210526315789473684210526315788, 1684210526315789473684210526315789473684210526315789473684210526315789472, 1894736842105263157894736842105263157894736842105263157894736842105263156]
[263157894736842105263157894736842105263157894736842105263157894736842105, 526315789473684210526315789473684210526315789473684210526315789473684210, 789473684210526315789473684210526315789473684210526315789473684210526315, 1052631578947368421052631578947368421052631578947368421052631578947368420, 1315789473684210526315789473684210526315789473684210526315789473684210525, 1578947368421052631578947368421052631578947368421052631578947368421052630, 1842105263157894736842105263157894736842105263157894736842105263157894735, 2105263157894736842105263157894736842105263157894736842105263157894736840, 2368421052631578947368421052631578947368421052631578947368421052631578945]
[315789473684210526315789473684210526315789473684210526315789473684210526, 631578947368421052631578947368421052631578947368421052631578947368421052, 947368421052631578947368421052631578947368421052631578947368421052631578, 1263157894736842105263157894736842105263157894736842105263157894736842104, 1578947368421052631578947368421052631578947368421052631578947368421052630, 1894736842105263157894736842105263157894736842105263157894736842105263156, 2210526315789473684210526315789473684210526315789473684210526315789473682, 2526315789473684210526315789473684210526315789473684210526315789473684208, 2842105263157894736842105263157894736842105263157894736842105263157894734]
[368421052631578947368421052631578947368421052631578947368421052631578947, 736842105263157894736842105263157894736842105263157894736842105263157894, 1105263157894736842105263157894736842105263157894736842105263157894736841, 1473684210526315789473684210526315789473684210526315789473684210526315788, 1842105263157894736842105263157894736842105263157894736842105263157894735, 2210526315789473684210526315789473684210526315789473684210526315789473682, 2578947368421052631578947368421052631578947368421052631578947368421052629, 2947368421052631578947368421052631578947368421052631578947368421052631576, 3315789473684210526315789473684210526315789473684210526315789473684210523]
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