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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Newman–Shanks–Williams prime ： ウィキペディア英語版 Newman–Shanks–Williams prime In mathematics, a Newman–Shanks–Williams prime (NSW prime) is a prime number ''p'' which can be written in the form :$S\_=\backslash frac\; +\; \backslash left(1\; -\; \backslash sqrt\backslash right)^\}.$ NSW primes were first described by Morris Newman, Daniel Shanks and Hugh C. Williams in 1981 during the study of finite simple groups with square order. The first few NSW primes are 7, 41, 239, 9369319, 63018038201, … , corresponding to the indices 3, 5, 7, 19, 29, … . The sequence ''S'' alluded to in the formula can be described by the following recurrence relation: :$S\_0=1\; \backslash ,$ :$S\_1=1\; \backslash ,$ :$S\_n=2S\_+S\_\backslash qquad\backslash textn\backslash geq\; 2.$ The first few terms of the sequence are 1, 1, 3, 7, 17, 41, 99, … . Each term in this sequence is half the corresponding term in the sequence of companion Pell numbers. These numbers also appear in the continued fraction convergents to √2. == Further reading == * 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「Newman–Shanks–Williams prime」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.