翻訳と辞書 Words near each other ・ Zeiraphera hohuanshana ・ Zeiraphera improbana ・ Zeiraphera isertana ・ Zeiraphera lariciana ・ Zeiraphera ratzeburgiana ・ Zeiraphera rufimitrana ・ Zeiraphera subcorticana ・ Zeiraphera taiwana ・ Zeiraphera thymelopa ・ Zeiraphera unfortunana ・ Zeiraphera virinea ・ Zeirath, Texas ・ Zeis ・ Zeise's salt ・ Zeisel determination ・ Zeisel number ・ Zeiselbach ・ Zeiselmauer-Wolfpassing ・ Zeishan Quadri ・ Zeiskam ・ Zeisler ・ Zeism ・ Zeiss ・ Zeiss (comics) ・ Zeiss Batis 1.8/85 ・ Zeiss Batis 2/25 ・ Zeiss Biogon ・ Zeiss formula ・ Zeiss Ikon Kolibri ・ Zeiss Loxia 2.8/21 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 Zeisel number ： ウィキペディア英語版 Zeisel number A Zeisel number, named after Helmut Zeisel, is a square-free integer ''k'' with at least three prime factors which fall into the pattern :$p\_x\; =\; ap\_\; +\; b$ where ''a'' and ''b'' are some integer constants and ''x'' is the index number of each prime factor in the factorization, sorted from lowest to highest. For the purpose of determining Zeisel numbers, $p\_0\; =\; 1$. The first few Zeisel numbers are :105, 1419, 1729, 1885, 4505, 5719, 15387, 24211, 25085, 27559, 31929, 54205, 59081, 114985, 207177, 208681, 233569, 287979, 294409, 336611, 353977, 448585, 507579, 982513, 1012121, 1073305, 1242709, 1485609, 2089257, 2263811, 2953711, … . To give an example, 1729 is a Zeisel number with the constants ''a'' = 1 and ''b'' = 6, its factors being 7, 13 and 19, falling into the pattern :$$ \begin p_1 = 7, & \quad p_3 = 1p_2 + 6 \end 1729 is an example for Carmichael numbers of the kind $(6n\; +\; 1)(12n\; +\; 1)(18n\; +\; 1)$, which satisfies the pattern $p\_x\; =\; ap\_\; +\; b$ with ''a''= 1 and ''b'' = 6n, so that every Carmichael number of the form (6n+1)(12n+1)(18n+1) is a Zeisel number. Other Carmichael numbers of that kind are: 294409, 56052361, 118901521, 172947529, 216821881, 228842209, 1299963601, 2301745249, 9624742921, … The name Zeisel numbers was probably introduced by Kevin Brown, who was looking for numbers that when plugged into the equation :$2^\; +\; k$ yield prime numbers. In a posting to the newsgroup sci.math on 1994-02-24, Helmut Zeisel pointed out that 1885 is one such number. Later it was discovered (by Kevin Brown?) that 1885 additionally has prime factors with the relationship described above, so a name like Brown-Zeisel Numbers might be more appropriate. Hardy Ramanujan's number 1729 is also a Zeisel number. ==Notes== 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「Zeisel 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.