2016年1月9日土曜日

160109(4)

Ruby


9 × (10^(18n) - 1) / 19 の性質について(3)

k × (10^(18n) - m) / 19 で
2, … , 18 倍すると大体数字がずれた状態になる
ものを選んでみた。
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
473684210526315789 × 10 = 4736842105263157890
473684210526315789 × 11 = 5210526315789473679
473684210526315789 × 12 = 5684210526315789468
473684210526315789 × 13 = 6157894736842105257
473684210526315789 × 14 = 6631578947368421046
473684210526315789 × 15 = 7105263157894736835
473684210526315789 × 16 = 7578947368421052624
473684210526315789 × 17 = 8052631578947368413
473684210526315789 × 18 = 8526315789473684202

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

n = 3
p ary = (0..n).inject([]){|s, i| s + (1..18).map{|k| f(k, i)}}.uniq!.sort
# それぞれj倍したもの
ary.each{|i| p (1..18).map{|j| i * j}}

出力結果
[0, 52631578947368421, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789, 526315789473684210, 578947368421052631, 631578947368421052, 684210526315789473, 736842105263157894, 789473684210526315, 842105263157894736, 894736842105263157, 947368421052631578, 52631578947368421052631578947368421, 105263157894736842105263157894736842, 157894736842105263157894736842105263, 210526315789473684210526315789473684, 263157894736842105263157894736842105, 315789473684210526315789473684210526, 368421052631578947368421052631578947, 421052631578947368421052631578947368, 473684210526315789473684210526315789, 526315789473684210526315789473684210, 578947368421052631578947368421052631, 631578947368421052631578947368421052, 684210526315789473684210526315789473, 736842105263157894736842105263157894, 789473684210526315789473684210526315, 842105263157894736842105263157894736, 894736842105263157894736842105263157, 947368421052631578947368421052631578, 52631578947368421052631578947368421052631578947368421, 105263157894736842105263157894736842105263157894736842, 157894736842105263157894736842105263157894736842105263, 210526315789473684210526315789473684210526315789473684, 263157894736842105263157894736842105263157894736842105, 315789473684210526315789473684210526315789473684210526, 368421052631578947368421052631578947368421052631578947, 421052631578947368421052631578947368421052631578947368, 473684210526315789473684210526315789473684210526315789, 526315789473684210526315789473684210526315789473684210, 578947368421052631578947368421052631578947368421052631, 631578947368421052631578947368421052631578947368421052, 684210526315789473684210526315789473684210526315789473, 736842105263157894736842105263157894736842105263157894, 789473684210526315789473684210526315789473684210526315, 842105263157894736842105263157894736842105263157894736, 894736842105263157894736842105263157894736842105263157, 947368421052631578947368421052631578947368421052631578]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[52631578947368421, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789, 526315789473684210, 578947368421052631, 631578947368421052, 684210526315789473, 736842105263157894, 789473684210526315, 842105263157894736, 894736842105263157, 947368421052631578]
[105263157894736842, 210526315789473684, 315789473684210526, 421052631578947368, 526315789473684210, 631578947368421052, 736842105263157894, 842105263157894736, 947368421052631578, 1052631578947368420, 1157894736842105262, 1263157894736842104, 1368421052631578946, 1473684210526315788, 1578947368421052630, 1684210526315789472, 1789473684210526314, 1894736842105263156]
[157894736842105263, 315789473684210526, 473684210526315789, 631578947368421052, 789473684210526315, 947368421052631578, 1105263157894736841, 1263157894736842104, 1421052631578947367, 1578947368421052630, 1736842105263157893, 1894736842105263156, 2052631578947368419, 2210526315789473682, 2368421052631578945, 2526315789473684208, 2684210526315789471, 2842105263157894734]
[210526315789473684, 421052631578947368, 631578947368421052, 842105263157894736, 1052631578947368420, 1263157894736842104, 1473684210526315788, 1684210526315789472, 1894736842105263156, 2105263157894736840, 2315789473684210524, 2526315789473684208, 2736842105263157892, 2947368421052631576, 3157894736842105260, 3368421052631578944, 3578947368421052628, 3789473684210526312]
[263157894736842105, 526315789473684210, 789473684210526315, 1052631578947368420, 1315789473684210525, 1578947368421052630, 1842105263157894735, 2105263157894736840, 2368421052631578945, 2631578947368421050, 2894736842105263155, 3157894736842105260, 3421052631578947365, 3684210526315789470, 3947368421052631575, 4210526315789473680, 4473684210526315785, 4736842105263157890]
[315789473684210526, 631578947368421052, 947368421052631578, 1263157894736842104, 1578947368421052630, 1894736842105263156, 2210526315789473682, 2526315789473684208, 2842105263157894734, 3157894736842105260, 3473684210526315786, 3789473684210526312, 4105263157894736838, 4421052631578947364, 4736842105263157890, 5052631578947368416, 5368421052631578942, 5684210526315789468]
[368421052631578947, 736842105263157894, 1105263157894736841, 1473684210526315788, 1842105263157894735, 2210526315789473682, 2578947368421052629, 2947368421052631576, 3315789473684210523, 3684210526315789470, 4052631578947368417, 4421052631578947364, 4789473684210526311, 5157894736842105258, 5526315789473684205, 5894736842105263152, 6263157894736842099, 6631578947368421046]
[421052631578947368, 842105263157894736, 1263157894736842104, 1684210526315789472, 2105263157894736840, 2526315789473684208, 2947368421052631576, 3368421052631578944, 3789473684210526312, 4210526315789473680, 4631578947368421048, 5052631578947368416, 5473684210526315784, 5894736842105263152, 6315789473684210520, 6736842105263157888, 7157894736842105256, 7578947368421052624]
[473684210526315789, 947368421052631578, 1421052631578947367, 1894736842105263156, 2368421052631578945, 2842105263157894734, 3315789473684210523, 3789473684210526312, 4263157894736842101, 4736842105263157890, 5210526315789473679, 5684210526315789468, 6157894736842105257, 6631578947368421046, 7105263157894736835, 7578947368421052624, 8052631578947368413, 8526315789473684202]
[526315789473684210, 1052631578947368420, 1578947368421052630, 2105263157894736840, 2631578947368421050, 3157894736842105260, 3684210526315789470, 4210526315789473680, 4736842105263157890, 5263157894736842100, 5789473684210526310, 6315789473684210520, 6842105263157894730, 7368421052631578940, 7894736842105263150, 8421052631578947360, 8947368421052631570, 9473684210526315780]
[578947368421052631, 1157894736842105262, 1736842105263157893, 2315789473684210524, 2894736842105263155, 3473684210526315786, 4052631578947368417, 4631578947368421048, 5210526315789473679, 5789473684210526310, 6368421052631578941, 6947368421052631572, 7526315789473684203, 8105263157894736834, 8684210526315789465, 9263157894736842096, 9842105263157894727, 10421052631578947358]
[631578947368421052, 1263157894736842104, 1894736842105263156, 2526315789473684208, 3157894736842105260, 3789473684210526312, 4421052631578947364, 5052631578947368416, 5684210526315789468, 6315789473684210520, 6947368421052631572, 7578947368421052624, 8210526315789473676, 8842105263157894728, 9473684210526315780, 10105263157894736832, 10736842105263157884, 11368421052631578936]
[684210526315789473, 1368421052631578946, 2052631578947368419, 2736842105263157892, 3421052631578947365, 4105263157894736838, 4789473684210526311, 5473684210526315784, 6157894736842105257, 6842105263157894730, 7526315789473684203, 8210526315789473676, 8894736842105263149, 9578947368421052622, 10263157894736842095, 10947368421052631568, 11631578947368421041, 12315789473684210514]
[736842105263157894, 1473684210526315788, 2210526315789473682, 2947368421052631576, 3684210526315789470, 4421052631578947364, 5157894736842105258, 5894736842105263152, 6631578947368421046, 7368421052631578940, 8105263157894736834, 8842105263157894728, 9578947368421052622, 10315789473684210516, 11052631578947368410, 11789473684210526304, 12526315789473684198, 13263157894736842092]
[789473684210526315, 1578947368421052630, 2368421052631578945, 3157894736842105260, 3947368421052631575, 4736842105263157890, 5526315789473684205, 6315789473684210520, 7105263157894736835, 7894736842105263150, 8684210526315789465, 9473684210526315780, 10263157894736842095, 11052631578947368410, 11842105263157894725, 12631578947368421040, 13421052631578947355, 14210526315789473670]
[842105263157894736, 1684210526315789472, 2526315789473684208, 3368421052631578944, 4210526315789473680, 5052631578947368416, 5894736842105263152, 6736842105263157888, 7578947368421052624, 8421052631578947360, 9263157894736842096, 10105263157894736832, 10947368421052631568, 11789473684210526304, 12631578947368421040, 13473684210526315776, 14315789473684210512, 15157894736842105248]
[894736842105263157, 1789473684210526314, 2684210526315789471, 3578947368421052628, 4473684210526315785, 5368421052631578942, 6263157894736842099, 7157894736842105256, 8052631578947368413, 8947368421052631570, 9842105263157894727, 10736842105263157884, 11631578947368421041, 12526315789473684198, 13421052631578947355, 14315789473684210512, 15210526315789473669, 16105263157894736826]
[947368421052631578, 1894736842105263156, 2842105263157894734, 3789473684210526312, 4736842105263157890, 5684210526315789468, 6631578947368421046, 7578947368421052624, 8526315789473684202, 9473684210526315780, 10421052631578947358, 11368421052631578936, 12315789473684210514, 13263157894736842092, 14210526315789473670, 15157894736842105248, 16105263157894736826, 17052631578947368404]
[52631578947368421052631578947368421, 105263157894736842105263157894736842, 157894736842105263157894736842105263, 210526315789473684210526315789473684, 263157894736842105263157894736842105, 315789473684210526315789473684210526, 368421052631578947368421052631578947, 421052631578947368421052631578947368, 473684210526315789473684210526315789, 526315789473684210526315789473684210, 578947368421052631578947368421052631, 631578947368421052631578947368421052, 684210526315789473684210526315789473, 736842105263157894736842105263157894, 789473684210526315789473684210526315, 842105263157894736842105263157894736, 894736842105263157894736842105263157, 947368421052631578947368421052631578]
[105263157894736842105263157894736842, 210526315789473684210526315789473684, 315789473684210526315789473684210526, 421052631578947368421052631578947368, 526315789473684210526315789473684210, 631578947368421052631578947368421052, 736842105263157894736842105263157894, 842105263157894736842105263157894736, 947368421052631578947368421052631578, 1052631578947368421052631578947368420, 1157894736842105263157894736842105262, 1263157894736842105263157894736842104, 1368421052631578947368421052631578946, 1473684210526315789473684210526315788, 1578947368421052631578947368421052630, 1684210526315789473684210526315789472, 1789473684210526315789473684210526314, 1894736842105263157894736842105263156]
[157894736842105263157894736842105263, 315789473684210526315789473684210526, 473684210526315789473684210526315789, 631578947368421052631578947368421052, 789473684210526315789473684210526315, 947368421052631578947368421052631578, 1105263157894736842105263157894736841, 1263157894736842105263157894736842104, 1421052631578947368421052631578947367, 1578947368421052631578947368421052630, 1736842105263157894736842105263157893, 1894736842105263157894736842105263156, 2052631578947368421052631578947368419, 2210526315789473684210526315789473682, 2368421052631578947368421052631578945, 2526315789473684210526315789473684208, 2684210526315789473684210526315789471, 2842105263157894736842105263157894734]
[210526315789473684210526315789473684, 421052631578947368421052631578947368, 631578947368421052631578947368421052, 842105263157894736842105263157894736, 1052631578947368421052631578947368420, 1263157894736842105263157894736842104, 1473684210526315789473684210526315788, 1684210526315789473684210526315789472, 1894736842105263157894736842105263156, 2105263157894736842105263157894736840, 2315789473684210526315789473684210524, 2526315789473684210526315789473684208, 2736842105263157894736842105263157892, 2947368421052631578947368421052631576, 3157894736842105263157894736842105260, 3368421052631578947368421052631578944, 3578947368421052631578947368421052628, 3789473684210526315789473684210526312]
[263157894736842105263157894736842105, 526315789473684210526315789473684210, 789473684210526315789473684210526315, 1052631578947368421052631578947368420, 1315789473684210526315789473684210525, 1578947368421052631578947368421052630, 1842105263157894736842105263157894735, 2105263157894736842105263157894736840, 2368421052631578947368421052631578945, 2631578947368421052631578947368421050, 2894736842105263157894736842105263155, 3157894736842105263157894736842105260, 3421052631578947368421052631578947365, 3684210526315789473684210526315789470, 3947368421052631578947368421052631575, 4210526315789473684210526315789473680, 4473684210526315789473684210526315785, 4736842105263157894736842105263157890]
[315789473684210526315789473684210526, 631578947368421052631578947368421052, 947368421052631578947368421052631578, 1263157894736842105263157894736842104, 1578947368421052631578947368421052630, 1894736842105263157894736842105263156, 2210526315789473684210526315789473682, 2526315789473684210526315789473684208, 2842105263157894736842105263157894734, 3157894736842105263157894736842105260, 3473684210526315789473684210526315786, 3789473684210526315789473684210526312, 4105263157894736842105263157894736838, 4421052631578947368421052631578947364, 4736842105263157894736842105263157890, 5052631578947368421052631578947368416, 5368421052631578947368421052631578942, 5684210526315789473684210526315789468]
[368421052631578947368421052631578947, 736842105263157894736842105263157894, 1105263157894736842105263157894736841, 1473684210526315789473684210526315788, 1842105263157894736842105263157894735, 2210526315789473684210526315789473682, 2578947368421052631578947368421052629, 2947368421052631578947368421052631576, 3315789473684210526315789473684210523, 3684210526315789473684210526315789470, 4052631578947368421052631578947368417, 4421052631578947368421052631578947364, 4789473684210526315789473684210526311, 5157894736842105263157894736842105258, 5526315789473684210526315789473684205, 5894736842105263157894736842105263152, 6263157894736842105263157894736842099, 6631578947368421052631578947368421046]
[421052631578947368421052631578947368, 842105263157894736842105263157894736, 1263157894736842105263157894736842104, 1684210526315789473684210526315789472, 2105263157894736842105263157894736840, 2526315789473684210526315789473684208, 2947368421052631578947368421052631576, 3368421052631578947368421052631578944, 3789473684210526315789473684210526312, 4210526315789473684210526315789473680, 4631578947368421052631578947368421048, 5052631578947368421052631578947368416, 5473684210526315789473684210526315784, 5894736842105263157894736842105263152, 6315789473684210526315789473684210520, 6736842105263157894736842105263157888, 7157894736842105263157894736842105256, 7578947368421052631578947368421052624]
[473684210526315789473684210526315789, 947368421052631578947368421052631578, 1421052631578947368421052631578947367, 1894736842105263157894736842105263156, 2368421052631578947368421052631578945, 2842105263157894736842105263157894734, 3315789473684210526315789473684210523, 3789473684210526315789473684210526312, 4263157894736842105263157894736842101, 4736842105263157894736842105263157890, 5210526315789473684210526315789473679, 5684210526315789473684210526315789468, 6157894736842105263157894736842105257, 6631578947368421052631578947368421046, 7105263157894736842105263157894736835, 7578947368421052631578947368421052624, 8052631578947368421052631578947368413, 8526315789473684210526315789473684202]
[526315789473684210526315789473684210, 1052631578947368421052631578947368420, 1578947368421052631578947368421052630, 2105263157894736842105263157894736840, 2631578947368421052631578947368421050, 3157894736842105263157894736842105260, 3684210526315789473684210526315789470, 4210526315789473684210526315789473680, 4736842105263157894736842105263157890, 5263157894736842105263157894736842100, 5789473684210526315789473684210526310, 6315789473684210526315789473684210520, 6842105263157894736842105263157894730, 7368421052631578947368421052631578940, 7894736842105263157894736842105263150, 8421052631578947368421052631578947360, 8947368421052631578947368421052631570, 9473684210526315789473684210526315780]
[578947368421052631578947368421052631, 1157894736842105263157894736842105262, 1736842105263157894736842105263157893, 2315789473684210526315789473684210524, 2894736842105263157894736842105263155, 3473684210526315789473684210526315786, 4052631578947368421052631578947368417, 4631578947368421052631578947368421048, 5210526315789473684210526315789473679, 5789473684210526315789473684210526310, 6368421052631578947368421052631578941, 6947368421052631578947368421052631572, 7526315789473684210526315789473684203, 8105263157894736842105263157894736834, 8684210526315789473684210526315789465, 9263157894736842105263157894736842096, 9842105263157894736842105263157894727, 10421052631578947368421052631578947358]
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