Transwiki:走馬燈數

例子

六位數

${\displaystyle 142857\times 1=142857}$
${\displaystyle 142857\times 2=285714}$
${\displaystyle 142857\times 3=428571}$
${\displaystyle 142857\times 4=571428}$
${\displaystyle 142857\times 5=714285}$
${\displaystyle 142857\times 6=857142}$
${\displaystyle 142857\times 7=999999}$

十六位數

${\displaystyle 0588235294117647\times 1=0588235294117647}$
${\displaystyle 0588235294117647\times 2=1176470588235294}$
${\displaystyle 0588235294117647\times 3=1764705882352941}$
${\displaystyle 0588235294117647\times 4=2352941176470588}$
${\displaystyle 0588235294117647\times 5=2941176470588235}$
${\displaystyle 0588235294117647\times 6=3529411764705882}$
${\displaystyle 0588235294117647\times 7=4117647058823529}$
${\displaystyle 0588235294117647\times 8=4705882352941176}$
${\displaystyle 0588235294117647\times 9=5294117647058823}$
${\displaystyle 0588235294117647\times 10=5882352941176470}$
${\displaystyle 0588235294117647\times 11=6470588235294117}$
${\displaystyle 0588235294117647\times 12=7058823529411764}$
${\displaystyle 0588235294117647\times 13=7647058823529411}$
${\displaystyle 0588235294117647\times 14=8235294117647058}$
${\displaystyle 0588235294117647\times 15=8823529411764705}$
${\displaystyle 0588235294117647\times 16=9411764705882352}$
${\displaystyle 0588235294117647\times 17=9999999999999999}$

十八位數

${\displaystyle 052631578947368421\times 1=052631578947368421}$
${\displaystyle 052631578947368421\times 2=105263157894736842}$
${\displaystyle 052631578947368421\times 3=157894736842105263}$
${\displaystyle 052631578947368421\times 4=210526315789473684}$
${\displaystyle 052631578947368421\times 5=263157894736842105}$
${\displaystyle 052631578947368421\times 6=315789473684210526}$
${\displaystyle 052631578947368421\times 7=368421052631578947}$
${\displaystyle 052631578947368421\times 8=421052631578947368}$
${\displaystyle 052631578947368421\times 9=473684210526315789}$
${\displaystyle 052631578947368421\times 10=526315789473684210}$
${\displaystyle 052631578947368421\times 11=578947368421052631}$
${\displaystyle 052631578947368421\times 12=631578947368421052}$
${\displaystyle 052631578947368421\times 13=684210526315789473}$
${\displaystyle 052631578947368421\times 14=736842105263157894}$
${\displaystyle 052631578947368421\times 15=789473684210526315}$
${\displaystyle 052631578947368421\times 16=842105263157894736}$
${\displaystyle 052631578947368421\times 17=894736842105263157}$
${\displaystyle 052631578947368421\times 18=947368421052631578}$
${\displaystyle 052631578947368421\times 19=999999999999999999}$

二十二位數

${\displaystyle 0434782608695652173913\times 1=0434782608695652173913}$
${\displaystyle 0434782608695652173913\times 2=0869565217391304347826}$
${\displaystyle 0434782608695652173913\times 3=1304347826086956521739}$
${\displaystyle 0434782608695652173913\times 4=1739130434782608695652}$
${\displaystyle 0434782608695652173913\times 5=2173913043478260869565}$
${\displaystyle 0434782608695652173913\times 6=2608695652173913043478}$
${\displaystyle 0434782608695652173913\times 7=3043478260869565217391}$
${\displaystyle 0434782608695652173913\times 8=3478260869565217391304}$
${\displaystyle 0434782608695652173913\times 9=3913043478260869565217}$
${\displaystyle 0434782608695652173913\times 10=4347826086956521739130}$
${\displaystyle 0434782608695652173913\times 11=4782608695652173913043}$
${\displaystyle 0434782608695652173913\times 12=5217391304347826086956}$
${\displaystyle 0434782608695652173913\times 13=5652173913043478260869}$
${\displaystyle 0434782608695652173913\times 14=6086956521739130434782}$
${\displaystyle 0434782608695652173913\times 15=6521739130434782608695}$
${\displaystyle 0434782608695652173913\times 16=6956521739130434782608}$
${\displaystyle 0434782608695652173913\times 17=7391304347826086956521}$
${\displaystyle 0434782608695652173913\times 18=7826086956521739130434}$
${\displaystyle 0434782608695652173913\times 19=8260869565217391304347}$
${\displaystyle 0434782608695652173913\times 20=8695652173913043478260}$
${\displaystyle 0434782608695652173913\times 21=9130434782608695652173}$
${\displaystyle 0434782608695652173913\times 22=9565217391304347826086}$
${\displaystyle 0434782608695652173913\times 23=9999999999999999999999}$

非乘以1至n是原數的循環排列

076923

• 076923非走馬燈數,因為它不是乘以1至n都是原數的循環排例
• 076923乘以1至12有兩組不同的偱環排列,乘以13全部位都是9。
• 076923乘以1、3、4、9、10、12是「076923」的偱環排列。
• 076923乘以2、5、6、7、8、11是「153846」的循環排列。

「076923」的循環排列

${\displaystyle 076923\times 1=076923}$
${\displaystyle 076923\times 3=230769}$
${\displaystyle 076923\times 4=307692}$
${\displaystyle 076923\times 9=692307}$
${\displaystyle 076923\times 10=769230}$
${\displaystyle 076923\times 12=923076}$

「153846」的偱環排列

${\displaystyle 076923\times 2=153846}$
${\displaystyle 076923\times 5=384615}$
${\displaystyle 076923\times 6=461538}$
${\displaystyle 076923\times 7=538461}$
${\displaystyle 076923\times 8=615384}$
${\displaystyle 076923\times 11=846153}$

乘以13全部位都是9

${\displaystyle 076923\times 13=999999}$