循环数

一个n位的循环数的性质是它乘以1至n都是各个数字的循环排列 , 乘以(n+1)会出现纯位数 , 纯位数每个位都是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