循環數
一個n位的循環數的性質是它乘以1至n都是各個數字的循環排列 , 乘以(n+1)會出現純位數 , 純位數每個位都是9。
1/7 = 0.(142857)
1/17 = 0.(0588235294117647)
1/19 = 0.(052631578947368421)
1/23 = 0.(0434782608695652173913)
142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
142857 * 7 = 999999
588235294117647 * 1 = 588235294117647
588235294117647 * 2 = 1176470588235294
588235294117647 * 3 = 1764705882352941
588235294117647 * 4 = 2352941176470588
588235294117647 * 5 = 2941176470588235
588235294117647 * 6 = 3529411764705882
588235294117647 * 7 = 4117647058823529
588235294117647 * 8 = 4705882352941176
588235294117647 * 9 = 5294117647058823
588235294117647 * 10 = 5882352941176470
588235294117647 * 11 = 6470588235294117
588235294117647 * 12 = 7058823529411764
588235294117647 * 13 = 7647058823529411
588235294117647 * 14 = 8235294117647058
588235294117647 * 15 = 8823529411764705
588235294117647 * 16 = 9411764705882352
588235294117647 * 17 = 9999999999999999
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
52631578947368421 * 10 = 526315789473684210
52631578947368421 * 11 = 578947368421052631
52631578947368421 * 12 = 631578947368421052
52631578947368421 * 13 = 684210526315789473
52631578947368421 * 14 = 736842105263157894
52631578947368421 * 15 = 789473684210526315
52631578947368421 * 16 = 842105263157894736
52631578947368421 * 17 = 894736842105263157
52631578947368421 * 18 = 947368421052631578
52631578947368421 * 19 = 999999999999999999
434782608695652173913 * 1 = 434782608695652173913
434782608695652173913 * 2 = 869565217391304347826
434782608695652173913 * 3 = 1304347826086956521739
434782608695652173913 * 4 = 1739130434782608695652
434782608695652173913 * 5 = 2173913043478260869565
434782608695652173913 * 6 = 2608695652173913043478
434782608695652173913 * 7 = 3043478260869565217391
434782608695652173913 * 8 = 3478260869565217391304
434782608695652173913 * 9 = 3913043478260869565217
434782608695652173913 * 10 = 4347826086956521739130
434782608695652173913 * 11 = 4782608695652173913043
434782608695652173913 * 12 = 5217391304347826086956
434782608695652173913 * 13 = 5652173913043478260869
434782608695652173913 * 14 = 6086956521739130434782
434782608695652173913 * 15 = 6521739130434782608695
434782608695652173913 * 16 = 6956521739130434782608
434782608695652173913 * 17 = 7391304347826086956521
434782608695652173913 * 18 = 7826086956521739130434
434782608695652173913 * 19 = 8260869565217391304347
434782608695652173913 * 20 = 8695652173913043478260
434782608695652173913 * 21 = 9130434782608695652173
434782608695652173913 * 22 = 9565217391304347826086
434782608695652173913 * 23 = 9999999999999999999999