Transwiki:走马灯数

走马灯数,指一个n位数乘以1至n是原数的偱环排列,乘以n+1全部位都是9。

例子

六位数

$142857\times 1=142857$

$142857\times 2=285714$

$142857\times 3=428571$

$142857\times 4=571428$

$142857\times 5=714285$

$142857\times 6=857142$

$142857\times 7=999999$

十六位数

$0588235294117647\times 1=0588235294117647$

$0588235294117647\times 2=1176470588235294$

$0588235294117647\times 3=1764705882352941$

$0588235294117647\times 4=2352941176470588$

$0588235294117647\times 5=2941176470588235$

$0588235294117647\times 6=3529411764705882$

$0588235294117647\times 7=4117647058823529$

$0588235294117647\times 8=4705882352941176$

$0588235294117647\times 9=5294117647058823$

$0588235294117647\times 10=5882352941176470$

$0588235294117647\times 11=6470588235294117$

$0588235294117647\times 12=7058823529411764$

$0588235294117647\times 13=7647058823529411$

$0588235294117647\times 14=8235294117647058$

$0588235294117647\times 15=8823529411764705$

$0588235294117647\times 16=9411764705882352$

$0588235294117647\times 17=9999999999999999$

十八位数

$052631578947368421\times 1=052631578947368421$

$052631578947368421\times 2=105263157894736842$

$052631578947368421\times 3=157894736842105263$

$052631578947368421\times 4=210526315789473684$

$052631578947368421\times 5=263157894736842105$

$052631578947368421\times 6=315789473684210526$

$052631578947368421\times 7=368421052631578947$

$052631578947368421\times 8=421052631578947368$

$052631578947368421\times 9=473684210526315789$

$052631578947368421\times 10=526315789473684210$

$052631578947368421\times 11=578947368421052631$

$052631578947368421\times 12=631578947368421052$

$052631578947368421\times 13=684210526315789473$

$052631578947368421\times 14=736842105263157894$

$052631578947368421\times 15=789473684210526315$

$052631578947368421\times 16=842105263157894736$

$052631578947368421\times 17=894736842105263157$

$052631578947368421\times 18=947368421052631578$

$052631578947368421\times 19=999999999999999999$

二十二位数

$0434782608695652173913\times 1=0434782608695652173913$

$0434782608695652173913\times 2=0869565217391304347826$

$0434782608695652173913\times 3=1304347826086956521739$

$0434782608695652173913\times 4=1739130434782608695652$

$0434782608695652173913\times 5=2173913043478260869565$

$0434782608695652173913\times 6=2608695652173913043478$

$0434782608695652173913\times 7=3043478260869565217391$

$0434782608695652173913\times 8=3478260869565217391304$

$0434782608695652173913\times 9=3913043478260869565217$

$0434782608695652173913\times 10=4347826086956521739130$

$0434782608695652173913\times 11=4782608695652173913043$

$0434782608695652173913\times 12=5217391304347826086956$

$0434782608695652173913\times 13=5652173913043478260869$

$0434782608695652173913\times 14=6086956521739130434782$

$0434782608695652173913\times 15=6521739130434782608695$

$0434782608695652173913\times 16=6956521739130434782608$

$0434782608695652173913\times 17=7391304347826086956521$

$0434782608695652173913\times 18=7826086956521739130434$

$0434782608695652173913\times 19=8260869565217391304347$

$0434782608695652173913\times 20=8695652173913043478260$

$0434782608695652173913\times 21=9130434782608695652173$

$0434782608695652173913\times 22=9565217391304347826086$

$0434782608695652173913\times 23=9999999999999999999999$

非乘以1至n是原数的循环排列

76923

• 76923非走马灯数,因为它不是乘以1至n都是原数的循环排列
• 76923乘以1至12有两组不同的偱环排列,乘以13全部位都是9。
• 76923乘以1、3、4、9、10、12是“76923”的偱环排列。
• 76923乘以2、5、6、7、8、11是“153846”的循环排列。

“76923”的循环排列

$76923\times 1=76923$

$76923\times 3=230769$

$76923\times 4=307692$

$76923\times 9=692307$

$76923\times 10=769230$

$76923\times 12=923076$

“153846”的偱环排列

$76923\times 2=153846$

$76923\times 5=384615$

$76923\times 6=461538$

$76923\times 7=538461$

$76923\times 8=615384$

$76923\times 11=846153$

乘以13全部位都是9

$76923\times 13=999999$