翻訳と辞書 Words near each other ・ Parastasia ・ Parastasia ephippium ・ Parastatal Sector Reform Commission ・ Parastathes ・ Parastathes apicalis ・ Parasitic disease ・ Parasitic drag ・ Parasitic element (electrical networks) ・ Parasitic extraction ・ Parasitic gap ・ Parasitic jaeger ・ Parasitic life cycles ・ Parasitic load ・ Parasitic loss ・ Parasitic mass ・ Parasitic number ・ Parasitic nutrition ・ Parasitic oscillation ・ Parasitic People ・ Parasitic plant ・ Parasitic pneumonia ・ Parasitic structure ・ Parasitic twin ・ Parasitic worm (disambiguation) ・ Parasitidae ・ Parasitiformes ・ Parasitiphis ・ Parasitism ・ Parasitism (social offense) ・ Parasitoid Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Parasitic number ： ウィキペディア英語版 Parasitic number An ''n''-parasitic number (in base 10) is a positive natural number which can be multiplied by ''n'' by moving the rightmost digit of its decimal representation to the front. Here ''n'' is itself a single-digit positive natural number. In other words, the decimal representation undergoes a right circular shift by one place. For example, 4•128205=512820, so 128205 is 4-parasitic. Most authors do not allow leading zeros to be used, and this article follows that convention. So even though 4•025641=102564, the number 025641 is ''not'' 4-parasitic. == Derivation == An ''n''-parasitic number can be derived by starting with a digit ''k'' (which should be equal to ''n'' or greater) in the rightmost (units) place, and working up one digit at a time. For example, for ''n'' = 4 and ''k'' = 7 :4•7=28 :4•87=348 :4•487=1948 :4•9487=37948 :4•79487=317948 :4•179487=717948. So 179487 is a 4-parasitic number with units digit 7. Others are 179487179487, 179487179487179487, etc. Notice that the repeating decimal :$x=0.179487179487179487\backslash ldots=0.\backslash overline\; \backslash mbox4x=0.\backslash overline=\backslash frac.$ Thus :$4x=\backslash frac\; \backslash mbox\; x=\backslash frac.$ In general, an ''n''-parasitic number can be found as follows. Pick a one digit integer ''k'' such that , and take the period of the repeating decimal ''k''/(10''n''−1). This will be $\backslash frac(10^m-1)$ where ''m'' is the length of the period; i.e. the multiplicative order of 10 modulo . For another example, if ''n'' = 2, then 10''n'' − 1 = 19 and the repeating decimal for 1/19 is : $\backslash frac=0.\backslash overline.$ So that for 2/19 is double that: : $\backslash frac=0.\backslash overline.$ The length ''m'' of this period is 18, the same as the order of 10 modulo 19, so = 105263157894736842. 105263157894736842 × 2 = 210526315789473684, which is the result of moving the last digit of 105263157894736842 to the front. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Parasitic number」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.