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Line 1: − The number '''142857''' has the curious property that, if it is multiplied by any number from 1 to 6, the result is a number with the same digits in the same order (a [[cyclic permutation]]). + − − For example: − :142857 × 1 = 142857 − :142857 × 2 = 285714 − :142857 × 3 = 428571 − :142857 × 4 = 571428 − :142857 × 5 = 714285 − :142857 × 6 = 857142 − − − This property is closely related to the facts that − :1/7 = 142857/999999 − − and that 1/7 expressed as a [[decimal]] is − − :0.142857142857142857142857142857... − − Investigating the number 142857 can lead a student into an understanding of repeating decimals and [[rational numbers]]. − − − == Similar Numbers == − 142857 is the only multi-digit decimal number with this property. However, if leading zeros are allowed on a number, some other examples are: − :0588235294117647 (16 digits) − :052631578947368421 (18 digits) − :0434782608695652173913 (22 digits) − :0344827586206896551724137931 (28 digits) − :0212765957446808510638297872340425531914893617 (46 digits) − − In octal (base-8 notation), the numbers 25 and 1463 have this property. There are no examples in hexadecimal (base-16). − − − − − − [[Category:Mathematics]]
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so what?