查看“︁142857”︁的源代码

{{noteTA|G1=Math}}
{{整数
| list = [[100000|<<]] 142856 '''142857''' 142858 ...[[144000]]... [[1000000|>>]]
| 小写 = 十四萬二千八百五十七
| 大写 = 拾肆萬貳仟捌佰伍拾柒
}}
'''142857'''（十四万二千八百五十七）是介于142856和142858之间的[[整数]]，是一個[[卡布列克數]]<ref>{{Cite web|url=https://oeis.org/A006886|title=Sloane's A006886: Kaprekar numbers|website=[[The On-Line Encyclopedia of Integer Sequences]]|publisher=OEIS Foundation|access-date=2016-06-03|archive-date=2022-12-18|archive-url=https://web.archive.org/web/20221218131152/https://oeis.org/A006886|dead-url=no}}</ref>。

142857是七分之一的前6位數（{{sfrac|1|7}}=0.{{overline|142857}}），也是十進制中最常見的[[循环数]]。<ref>{{cite web|url=http://www.daviddarling.info/encyclopedia/C/cyclic_number.html |title=Cyclic number |archive-url=https://web.archive.org/web/20070929122525/http://www.daviddarling.info/encyclopedia/C/cyclic_number.html |archive-date=2007-09-29 |website=The Internet Encyclopedia of Science}}</ref><ref>{{cite journal|first=Michael W. |last=Ecker |jstor=3026586 |title=The Alluring Lore of Cyclic Numbers |journal=The Two-Year College Mathematics Journal |volume=14 |issue=2 |date=March 1983 |pages=105–109|doi=10.2307/3026586 }}</ref><ref>{{cite web|url=http://planetmath.org/encyclopedia/CyclicNumber.html |title=Cyclic number |archive-url=https://web.archive.org/web/20070714114415/http://planetmath.org/encyclopedia/CyclicNumber.html |archive-date=2007-07-14 |website=PlanetMath}}</ref><ref>{{cite web |url=http://findarticles.com/p/articles/mi_hb4870/is_200508/ai_n17913296 |archive-url=https://web.archive.org/web/20071224191059/http://findarticles.com/p/articles/mi_hb4870/is_200508/ai_n17913296 |url-status=dead |archive-date=2007-12-24 |title=Go figure (cyclic numbers) |last=Hogan |first=Kathryn |website=Australian Doctor |date=August 2005 }}</ref>

== 性质 ==
=== 一般性質 ===
{{數字性質|use math=yes}}

=== 特殊性质 ===
* 用142857分别乘以[[1]]、[[2]]、[[3]]、[[4]]、[[5]]、[[6]]这几个数，其[[乘法|积]]仍由原来的1、4、2、8、5、7六个数组成，只是排列不同（称为[[循环数]]）。
:142857×1=142857
:142857×2=285714
:142857×3=428571
:142857×4=571428
:142857×5=714285
:142857×6=857142
:142857×7=999999

把142857這個數字分解成兩組數字：142、857。這兩個數字之和得出999。<br>
或把142857分解成三組數字：14、28、57。這三組數字之和得出99。<br>
假如把142857自乘，結果是20408122449，將此數分解兩組數字：20408和122449。它們之和是142857。<br>

能被7整除的自然数的个数
* 10以内 1个
* 100以内 14个
* 1000以内 142个
* 10000以内 1428个
* 100000以内 14285个
* 1000000以内 142857个
* 10000000以内 1428571个
......

用[[1]]至[[9]]除以[[7]]之後獲得的[[循环小数]]，循環的數字也是142857（7除以7除外）：

: 1 ÷ 7 = 0.<span style="text-decoration: overline;">142857</span>
: 2 ÷ 7 = 0.<span style="text-decoration: overline;">285714</span>
: 3 ÷ 7 = 0.<span style="text-decoration: overline;">428571</span>
: 4 ÷ 7 = 0.<span style="text-decoration: overline;">571428</span>
: 5 ÷ 7 = 0.<span style="text-decoration: overline;">714285</span>
: 6 ÷ 7 = 0.<span style="text-decoration: overline;">857142</span>
: 7 ÷ 7 = 1.<span style="text-decoration: overline;">000000</span>
: 8 ÷ 7 = 1.<span style="text-decoration: overline;">142857</span>
: 9 ÷ 7 = 1.<span style="text-decoration: overline;">285714</span>

用[[22]]除以[[7]]更可獲得[[圓周率]]古代的近似值：

: 22 ÷ 7 = 3.<span style="text-decoration: overline;">142857</span>

: <math>\frac{1}{7} = \sum_{n=0}^\infty 3^{n} * 10^{-(n+1)}</math>

[[Category:整数]]