翻訳と辞書 Words near each other ・ Carol Toscano ・ Carol Townend ・ Carol Truax ・ Carol Morris ・ Carol Moseke ・ Carol Moseley Braun ・ Carol Mujokoro ・ Carol Murphy ・ Carol Muske-Dukes ・ Carol Mutter ・ Carol Myers-Scotton ・ Carol Neblett ・ Carol Newinn ・ Carol Noonan ・ Carol Nugent ・ Carol number ・ Carol O'Connell ・ Carol O'Leary ・ Carol of Harvest ・ Carol of the Bells ・ Carol of the Old Ones ・ Carol Off ・ Carol Ohmart ・ Carol Owens ・ Carol Owens (politician) ・ Carol Owens (squash player) ・ Carol Oyler ・ Carol Padden ・ Carol Parc Hotel ・ Carol Park 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 Carol number ： ウィキペディア英語版 Carol number A Carol number is an integer of the form $4^n\; -\; 2^\; -\; 1$. An equivalent formula is $(2^n\; -\; 1)^2\; -\; 2$. The first few Carol numbers are: −1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527 . Carol numbers were first studied by Cletus Emmanuel, who named them after a friend, Carol G. Kirnon.〔(Cletus Emmanuel ) at Prime Pages〕〔(Message to Yahoo primenumbers group ) from Cletus Emmanuel〕 ==Binary representation== For ''n'' > 2, the binary representation of the ''n''-th Carol number is ''n'' − 2 consecutive ones, a single zero in the middle, and ''n'' + 1 more consecutive ones, or to put it algebraically, :$\backslash sum\_^\; 2^.$ So, for example, 47 is 101111 in binary, 223 is 11011111, etc. The difference between the 2''n''-th Mersenne number and the ''n''-th Carol number is $2^$. This gives yet another equivalent expression for Carol numbers, $(2^\; -\; 1)\; -\; 2^$. The difference between the ''n''-th Kynea number and the ''n''-th Carol number is the (''n'' + 2)th power of two. 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「Carol 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.