. . . . . . "\u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217\u7684\u5B9A\u7FA9\u70BA\u3002\u7576\uFF0C\u7531\u65BC\u7A7A\u7A4D\uFF08\u4E00\u500B\u7A7A\u96C6\u5167\u6240\u6709\u5143\u7D20\u7684\u7A4D\uFF09\u662F\uFF0C\u6240\u4EE5\uFF0C\u4E4B\u5F8C\u662F\uFF08\uFF09 \u9019\u4EA6\u53EF\u4EE5\u7528\u905E\u6B78\u5B9A\u7FA9\uFF1A\u3002 \u4EE5\u6578\u5B78\u6B78\u7D0D\u6CD5\u53EF\u8B49\u660E\u3002 \u300C\u6C42\u500B\u57C3\u53CA\u5206\u6578\uFF0C\u4F7F\u5B83\u5011\u4E4B\u548C\u6700\u63A5\u8FD1\u800C\u53C8\u5C0F\u65BC\u3002\u300D\u7B54\u6848\u5C31\u662F\u9019\u6578\u5217\u4E2D\u9996\u500B\u6578\u7684\u5012\u6578\u4E4B\u548C\u3002[1]\u56E0\u6B64\uFF0C\u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217\u53C8\u53EF\u4EE5\u8CAA\u5A6A\u7B97\u6CD5\u4F86\u5B9A\u7FA9\uFF1A\u6BCF\u6B65\u9078\u53D6\u7684\u4E00\u500B\u5206\u6BCD\uFF0C\u4F7F\u5F97\u5C0D\u61C9\u7684\u57C3\u53CA\u5206\u6578\u518D\u52A0\u4E0A\u4E4B\u524D\u7684\u548C\u6700\u63A5\u8FD11\u800C\u53C8\u5C11\u65BC1\u3002 \u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217\u53EF\u4EE5\u8868\u793A\u70BA\uFF0C\u5176\u4E2DE\u7D04\u70BA1.264\u3002\u9019\u548C\u8CBB\u99AC\u6578\u5F88\u76F8\u4F3C\u3002 \u9019\u6578\u5217\u4EE5\u8A79\u59C6\u65AF\u00B7\u7D04\u745F\u592B\u00B7\u897F\u723E\u7DAD\u65AF\u7279\u547D\u540D\u3002"@zh . . . . . "Sylvestrova posloupnost, pojmenovan\u00E1 po Jamesovi Sylvesterovi, je matematick\u00E1 posloupnost cel\u00FDch \u010D\u00EDsel definovan\u00E1 tak, \u017Ee ka\u017Ed\u00FD prvek posloupnosti je sou\u010Dinem p\u0159edch\u00E1zej\u00EDc\u00EDch prvk\u016F plus jedna. Form\u00E1ln\u011B se definuje jako p\u0159i\u010Dem\u017E nult\u00FD \u010Dlen posloupnosti je 2, jeliko\u017E pr\u00E1zdn\u00FD sou\u010Din m\u00E1 hodnotu 1. Alternativn\u011B m\u016F\u017Ee b\u00FDt posloupnost definov\u00E1na i pomoc\u00ED kde s0 = 2."@cs . . "David Raymond Curtiss"@en . . "1922"^^ . . . . . . . . "Sylvesters talf\u00F6ljd \u00E4r en talf\u00F6ljd d\u00E4r varje tal i f\u00F6ljden \u00E4r produkten av de f\u00F6reg\u00E5ende talen plus ett, d\u00E4r det f\u00F6rsta talet \u00E4r 2. De f\u00F6rsta talen i serien \u00E4r: 2, 3, 7, 43, , , , ,... Talf\u00F6ljden \u00E4r uppkallad efter James Joseph Sylvester."@sv . . . . . "\u041F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0421\u0438\u043B\u044C\u0432\u0435\u0441\u0442\u0440\u0430 \u2014 , \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043A\u0430\u0436\u0434\u044B\u0439 \u043E\u0447\u0435\u0440\u0435\u0434\u043D\u043E\u0439 \u0447\u043B\u0435\u043D \u0440\u0430\u0432\u0435\u043D \u043F\u0440\u043E\u0438\u0437\u0432\u0435\u0434\u0435\u043D\u0438\u044E \u043F\u0440\u0435\u0434\u044B\u0434\u0443\u0449\u0438\u0445 \u0447\u043B\u0435\u043D\u043E\u0432 \u043F\u043B\u044E\u0441 \u0435\u0434\u0438\u043D\u0438\u0446\u0430. \u041F\u0435\u0440\u0432\u044B\u0435 \u043D\u0435\u0441\u043A\u043E\u043B\u044C\u043A\u043E \u0447\u043B\u0435\u043D\u043E\u0432 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438: 2, 3, 7, 43, 1807, 3 263 443, 10 650 056 950 807, 113 423 713 055 421 850 000 000 000, \u2026 (\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0432 OEIS). \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043F\u043E \u0438\u043C\u0435\u043D\u0438 \u0414\u0436\u0435\u0439\u043C\u0441\u0430 \u0421\u0438\u043B\u044C\u0432\u0435\u0441\u0442\u0440\u0430, \u043A\u043E\u0442\u043E\u0440\u044B\u0439 \u043F\u0435\u0440\u0432\u044B\u043C \u0438\u0441\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u043B \u0435\u0451 \u0432 1880 \u0433\u043E\u0434\u0443. \u0417\u043D\u0430\u0447\u0435\u043D\u0438\u044F \u0435\u0451 \u0447\u043B\u0435\u043D\u043E\u0432 \u0440\u0430\u0441\u0442\u0443\u0442 \u043A\u0430\u043A , \u0430 \u0441\u0443\u043C\u043C\u0430 \u043E\u0431\u0440\u0430\u0442\u043D\u044B\u0445 \u0447\u043B\u0435\u043D\u043E\u0432 \u043E\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0440\u044F\u0434 \u0434\u043E\u043B\u0435\u0439 \u0435\u0434\u0438\u043D\u0438\u0446\u044B, \u043A\u043E\u0442\u043E\u0440\u044B\u0439 \u0441\u0445\u043E\u0434\u0438\u0442\u0441\u044F \u043A 1 \u0431\u044B\u0441\u0442\u0440\u0435\u0435, \u0447\u0435\u043C \u043B\u044E\u0431\u043E\u0439 \u0434\u0440\u0443\u0433\u043E\u0439 \u0440\u044F\u0434 \u0434\u0440\u043E\u0431\u0435\u0439 \u0435\u0434\u0438\u043D\u0438\u0446\u044B \u0441 \u0442\u0435\u043C \u0436\u0435 \u0447\u0438\u0441\u043B\u043E\u043C \u0447\u043B\u0435\u043D\u043E\u0432. \u0420\u0435\u043A\u0443\u0440\u0440\u0435\u043D\u0442\u043D\u043E\u0435 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u0435, \u043A\u043E\u0442\u043E\u0440\u043E\u0435 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u0447\u043B\u0435\u043D\u044B \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438, \u043F\u043E\u0437\u0432\u043E\u043B\u044F\u0435\u0442 \u0447\u0438\u0441\u043B\u0430\u043C \u0432 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438 \u0431\u044B\u0442\u044C \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u043D\u044B\u043C\u0438 \u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u0442\u0435\u043B\u0438 \u043F\u0440\u043E\u0449\u0435, \u043D\u0435\u0436\u0435\u043B\u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0447\u0438\u0441\u043B\u0430 \u0442\u043E\u0433\u043E \u0436\u0435 \u043F\u043E\u0440\u044F\u0434\u043A\u0430, \u043D\u043E \u0432\u0432\u0438\u0434\u0443 \u043E\u0447\u0435\u043D\u044C \u0431\u044B\u0441\u0442\u0440\u043E\u0433\u043E \u0440\u043E\u0441\u0442\u0430 \u0447\u043B\u0435\u043D\u043E\u0432 \u0440\u044F\u0434\u0430 \u043F\u043E\u043B\u043D\u043E\u0435 \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u043D\u0430 \u043F\u0440\u043E\u0441\u0442\u044B\u0435 \u043C\u043D\u043E\u0436\u0438\u0442\u0435\u043B\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u043D\u043E \u0442\u043E\u043B\u044C\u043A\u043E \u0434\u043B\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0447\u043B\u0435\u043D\u043E\u0432 \u044D\u0442\u043E\u0439 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438. \u0417\u043D\u0430\u0447\u0435\u043D\u0438\u044F, \u043F\u043E\u043B\u0443\u0447\u0435\u043D\u043D\u044B\u0435 \u0441 \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043D\u0438\u0435\u043C \u044D\u0442\u043E\u0439 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u044E\u0442\u0441\u044F \u0434\u043B\u044F \u043E\u0431\u0440\u0430\u0437\u043E\u0432\u0430\u043D\u0438\u044F \u043A\u043E\u043D\u0435\u0447\u043D\u043E\u0433\u043E \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u0435\u043D\u0438\u044F 1 \u0432 \u0432\u0438\u0434\u0435 \u0435\u0433\u0438\u043F\u0435\u0442\u0441\u043A\u043E\u0439 \u0434\u0440\u043E\u0431\u0438, \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0439 \u042D\u0439\u043D\u0448\u0442\u0435\u0439\u043D\u0430 \u0438 \u043A\u0430\u043A \u0438\u0441\u0442\u043E\u0447\u043D\u0438\u043A \u0434\u0430\u043D\u043D\u044B\u0445 \u0434\u043B\u044F ."@ru . . . "En teor\u00EDa de n\u00FAmeros, la sucesi\u00F3n de Sylvester es una sucesi\u00F3n de n\u00FAmeros enteros en la cual cada t\u00E9rmino es el producto de todos los anteriores, m\u00E1s uno. Los primeros t\u00E9rminos de la sucesi\u00F3n son: 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 . La sucesi\u00F3n de Sylvester se llama as\u00ED en honor de James Joseph Sylvester, quien la investig\u00F3 por primera vez en 1880. Sus t\u00E9rminos crecen de forma , y la suma de sus inversos constituye una serie de fracciones unitarias que converge a 1 m\u00E1s r\u00E1pidamente que ninguna otra serie de fracciones unitarias con la misma suma. La manera en que se define permite que sus t\u00E9rminos se factoricen m\u00E1s f\u00E1cilmente que otros n\u00FAmeros del mismo orden de magnitud, pero, debido al ritmo de crecimiento de los mismos, s\u00F3lo se conoce la factorizaci\u00F3n completa en factores primos de unos pocos t\u00E9rminos. Los t\u00E9rminos de esta sucesi\u00F3n tambi\u00E9n han tenido usos en la representaci\u00F3n finita de fracciones egipcias de suma 1, as\u00ED como en las y las ."@es . . . . . "Sucesi\u00F3n de Sylvester"@es . . "In number theory, Sylvester's sequence is an integer sequence in which each term of the sequence is the product of the previous terms, plus one. The first few terms of the sequence are 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (sequence in the OEIS). Sylvester's sequence is named after James Joseph Sylvester, who first investigated it in 1880. Its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions. The recurrence by which it is defined allows the numbers in the sequence to be factored more easily than other numbers of the same magnitude, but, due to the rapid growth of the sequence, complete prime factorizations are known only for a few of its terms. Values derived from this sequence have also been used to construct finite Egyptian fraction representations of 1, Sasakian Einstein manifolds, and hard instances for online algorithms."@en . "En teor\u00EDa de n\u00FAmeros, la sucesi\u00F3n de Sylvester es una sucesi\u00F3n de n\u00FAmeros enteros en la cual cada t\u00E9rmino es el producto de todos los anteriores, m\u00E1s uno. Los primeros t\u00E9rminos de la sucesi\u00F3n son: 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 ."@es . . . "\u30B7\u30EB\u30D9\u30B9\u30BF\u30FC\u6570\u5217"@ja . . . . . . . . . "En th\u00E9orie des nombres, la suite de Sylvester est une suite d'entiers telle que chaque terme est le produit de tous les termes pr\u00E9c\u00E9dents augment\u00E9 de 1, en partant d'un terme initial \u00E9gal \u00E0 2. Les premiers termes de la suite sont : 2 ; 3 ; 7 ; 43 ; 1 807 ; 3 263 443 ; 10 650 056 950 807 ; 113 423 713 055 421 844 361 000 443 (Voir la suite de l'OEIS). En hommage \u00E0 la d\u00E9monstration par Euclide de l'infinitude des nombres premiers, les termes de cette suite sont aussi parfois appel\u00E9s \"nombres d'Euclide\". La suite de Sylvester doit son nom \u00E0 James Joseph Sylvester qui, le premier, \u00E9tudia ses propri\u00E9t\u00E9s dans les ann\u00E9es 1880. Ses termes pr\u00E9sentent une croissance exponentielle double. La s\u00E9rie form\u00E9e de la somme des inverses de cette suite converge vers 1, plus vite que toute autre s\u00E9rie somme infinie d'inverses d'entiers convergeant vers 1. La relation de r\u00E9currence qui d\u00E9finit les termes de la suite permet de factoriser ceux-ci plus facilement que toute autre s\u00E9rie de croissance comparable, mais, du fait de la croissance rapide de la s\u00E9rie, la d\u00E9composition en nombres premiers n'est connue que pour quelques termes. Des valeurs extraites de cette suite ont \u00E9t\u00E9 utilis\u00E9es pour construire des repr\u00E9sentations de 1 sous forme de d\u00E9veloppement en fractions \u00E9gyptiennes, et intervient dans l'\u00E9tude des vari\u00E9t\u00E9s d'Einstein (en)."@fr . . "Sylvester's Sequence"@en . . . . . . . . . . . "4535485"^^ . . . . . . . . "\u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217"@zh . . "SylvestersSequence"@en . . . . . . . . "Sylvester's sequence"@en . "\u041F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0421\u0438\u043B\u044C\u0432\u0435\u0441\u0442\u0440\u0430"@ru . . . . "En th\u00E9orie des nombres, la suite de Sylvester est une suite d'entiers telle que chaque terme est le produit de tous les termes pr\u00E9c\u00E9dents augment\u00E9 de 1, en partant d'un terme initial \u00E9gal \u00E0 2. Les premiers termes de la suite sont : 2 ; 3 ; 7 ; 43 ; 1 807 ; 3 263 443 ; 10 650 056 950 807 ; 113 423 713 055 421 844 361 000 443 (Voir la suite de l'OEIS). En hommage \u00E0 la d\u00E9monstration par Euclide de l'infinitude des nombres premiers, les termes de cette suite sont aussi parfois appel\u00E9s \"nombres d'Euclide\"."@fr . "\u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217\u7684\u5B9A\u7FA9\u70BA\u3002\u7576\uFF0C\u7531\u65BC\u7A7A\u7A4D\uFF08\u4E00\u500B\u7A7A\u96C6\u5167\u6240\u6709\u5143\u7D20\u7684\u7A4D\uFF09\u662F\uFF0C\u6240\u4EE5\uFF0C\u4E4B\u5F8C\u662F\uFF08\uFF09 \u9019\u4EA6\u53EF\u4EE5\u7528\u905E\u6B78\u5B9A\u7FA9\uFF1A\u3002 \u4EE5\u6578\u5B78\u6B78\u7D0D\u6CD5\u53EF\u8B49\u660E\u3002 \u300C\u6C42\u500B\u57C3\u53CA\u5206\u6578\uFF0C\u4F7F\u5B83\u5011\u4E4B\u548C\u6700\u63A5\u8FD1\u800C\u53C8\u5C0F\u65BC\u3002\u300D\u7B54\u6848\u5C31\u662F\u9019\u6578\u5217\u4E2D\u9996\u500B\u6578\u7684\u5012\u6578\u4E4B\u548C\u3002[1]\u56E0\u6B64\uFF0C\u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217\u53C8\u53EF\u4EE5\u8CAA\u5A6A\u7B97\u6CD5\u4F86\u5B9A\u7FA9\uFF1A\u6BCF\u6B65\u9078\u53D6\u7684\u4E00\u500B\u5206\u6BCD\uFF0C\u4F7F\u5F97\u5C0D\u61C9\u7684\u57C3\u53CA\u5206\u6578\u518D\u52A0\u4E0A\u4E4B\u524D\u7684\u548C\u6700\u63A5\u8FD11\u800C\u53C8\u5C11\u65BC1\u3002 \u897F\u723E\u7DAD\u65AF\u7279\u6578\u5217\u53EF\u4EE5\u8868\u793A\u70BA\uFF0C\u5176\u4E2DE\u7D04\u70BA1.264\u3002\u9019\u548C\u8CBB\u99AC\u6578\u5F88\u76F8\u4F3C\u3002 \u9019\u6578\u5217\u4EE5\u8A79\u59C6\u65AF\u00B7\u7D04\u745F\u592B\u00B7\u897F\u723E\u7DAD\u65AF\u7279\u547D\u540D\u3002"@zh . . . "En teoria dels nombres, la seq\u00FC\u00E8ncia de Sylvester \u00E9s una seq\u00FC\u00E8ncia d'enters en qu\u00E8 cada membre de la seq\u00FC\u00E8ncia \u00E9s el producte dels membres anteriors m\u00E9s u. Els primers termes de la seq\u00FC\u00E8ncia s\u00F3n:2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (successi\u00F3 A000058 a l'OEIS). La seq\u00FC\u00E8ncia de Sylvester pren el nom de James Joseph Sylvester, qui la investig\u00E0 per primera vegada el 1880. Els seus valors creixen , i la suma dels seus forma una s\u00E8rie de fraccions unit\u00E0ries que convergeix a la unitat m\u00E9s aviat que qualsevol altra s\u00E8rie de fraccions unit\u00E0ries amb la mateixa suma. La recurr\u00E8ncia que la defineix permet una Factoritzaci\u00F3 m\u00E9s senzilla que la d'altres nombres qualssevol de la mateixa mida, per\u00F2, a causa del r\u00E0pid creixement de la seq\u00FC\u00E8ncia, nom\u00E9s es coneixen les factoritzacions completes en nombres primeres d'alguns dels seus termes. Els valors derivats d'aquesta seq\u00FC\u00E8ncia s'han fet servir per construir representacions en fraccions egipcianes de suma 1, aix\u00ED com en i les ."@ca . . . . . . . . . . . . . "Seq\u00FC\u00E8ncia de Sylvester"@ca . . . . . "Successione di Sylvester"@it . . . . . . . . . . . . . . "\u041F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0421\u0438\u043B\u044C\u0432\u0435\u0441\u0442\u0440\u0430 \u2014 , \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043A\u0430\u0436\u0434\u044B\u0439 \u043E\u0447\u0435\u0440\u0435\u0434\u043D\u043E\u0439 \u0447\u043B\u0435\u043D \u0440\u0430\u0432\u0435\u043D \u043F\u0440\u043E\u0438\u0437\u0432\u0435\u0434\u0435\u043D\u0438\u044E \u043F\u0440\u0435\u0434\u044B\u0434\u0443\u0449\u0438\u0445 \u0447\u043B\u0435\u043D\u043E\u0432 \u043F\u043B\u044E\u0441 \u0435\u0434\u0438\u043D\u0438\u0446\u0430. \u041F\u0435\u0440\u0432\u044B\u0435 \u043D\u0435\u0441\u043A\u043E\u043B\u044C\u043A\u043E \u0447\u043B\u0435\u043D\u043E\u0432 \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u0438: 2, 3, 7, 43, 1807, 3 263 443, 10 650 056 950 807, 113 423 713 055 421 850 000 000 000, \u2026 (\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0432 OEIS)."@ru . . . "La successione di Sylvester \u00E8 formata dai denominatori coprimi di una frazione egiziana (essa \u00E8 la somma di frazioni che hanno al numeratore l'unit\u00E0 e al denomintore numeri interi positivi distinti fra loro, per esempio 1/2+1/3. Si dimostra che ogni numero razionale positivo, a/b, pu\u00F2 essere scritto come frazione egiziana). La somma delle frazioni ottenute mettendo al denominatore i numeri della successione di Sylvester tende ad 1. I suoi primi termini sono 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 . Possiamo quindi scrivere"@it . . "Curtiss"@en . "\uC218\uB860\uC5D0\uC11C \uC2E4\uBCA0\uC2A4\uD130 \uC218\uC5F4(Sylvester's sequence)\uC740 \uD2B9\uC218\uD55C \uC815\uC218 \uC21C\uC11C\uC778\uB370, \uC774 \uC21C\uC11C\uC5D0\uC11C \uAC01 \uAD6C\uC131\uC6D0\uC740 \uC774\uC804 \uAD6C\uC131\uC6D0\uC73C\uB85C\uBD80\uD130\uC758 \uC0DD\uC131\uBB3C\uB85C\uC11C \uC774\uC804 \uC21C\uC11C\uC218\uC758 \uACF1\uC5D0 1\uC744 \uB354\uD55C \uC218\uC774\uB2E4. \uC2DC\uD000\uC2A4(\uC218\uC5F4)\uC758 \uCC98\uC74C \uCD9C\uD604 \uBA87 \uAC00\uC9C0 \uAD6C\uC131\uC6D0\uC778 \uD56D\uB4E4\uC740 \uB2E4\uC74C\uACFC \uAC19\uB2E4. 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 , ...... (OEIS\uC758 \uC218\uC5F4 ) \uC2E4\uBCA0\uC2A4\uD130 \uC2DC\uD038\uC2A4\uB294 1880\uB144\uC5D0 \uADF8\uAC83\uC744 \uCC98\uC74C \uC870\uC0AC\uD55C \uC81C\uC784\uC2A4 \uC870\uC149 \uC2E4\uBCA0\uC2A4\uD130\uC758 \uC774\uB984\uC744 \uB530\uC11C \uC9C0\uC5B4\uC84C\uB2E4. \uC774\uAC83\uC758 \uAC00\uCE58\uB294 \uAE30\uD558\uAE09\uC218\uC801\uC778 \uBC30\uB85C \uC99D\uAC00\uD55C \uC218\uAC00 \uC18C\uC218\uC778 \uC810\uBFD0\uB9CC\uC544\uB2C8\uB77C \uADF8\uAC83\uC758 \uC655\uBCF5\uC120\uC0C1\uC758 \uC218\uC5F4 \uD56D\uC758 \uC0DD\uC131\uC740 \uB3D9\uC77C\uD55C \uAC1C\uC218\uC758 \uD56D\uB4E4\uC744 \uAC00\uC9C4 \uB2E4\uB978 \uB2E8\uC704\uBD84\uC218\uBCF4\uB2E4 \uB354 \uBE68\uB9AC 1\uB85C \uC218\uB834\uB418\uB294 \uC77C\uB828\uC758 \uC988\uB0A8 \uBB38\uC81C\uC640 \uAD00\uB828\uD55C \uB2E8\uC704\uBD84\uC218\uB97C \uD615\uC131\uD55C\uB2E4\uB294\uAC83\uC744 \uBCF4\uC5EC\uC900\uB2E4\uB294 \uC810\uC774\uB2E4. \uC798 \uC815\uC758\uB41C \uBC18\uBCF5\uC758 \uC810\uD654\uC2DD\uC740 \uB3D9\uC77C\uD55C \uD06C\uAE30\uC758 \uC2E4\uC81C \uC22B\uC790\uBCF4\uB2E4 \uC218\uC5F4\uC758 \uC22B\uC790\uB97C \uC27D\uAC8C \uBC18\uC601\uD560 \uC218 \uC788\uC9C0\uB9CC, \uC218\uC5F4\uC758 \uAE09\uC18D\uD55C \uC131\uC7A5\uC73C\uB85C \uC778\uD574 \uC0DD\uC131\uB418\uB294 \uC2E4\uC81C \uD070 \uC218\uB4E4 \uC18C\uC218\uB294 \uC798 \uC54C\uB824\uC838 \uC788\uC9C0 \uC54A\uB2E4. \uC774 \uC218\uC5F4\uB85C\uBD80\uD130 \uD30C\uC0DD\uB41C \uAC12\uC740 \uC0AC\uC0AC\uD0A4\uC548 \uC544\uC778\uC288\uD0C0\uC778 \uB2E4\uC591\uCCB4 \uBC0F \uC628\uB77C\uC778 \uC54C\uACE0\uB9AC\uC998\uC758 \uB09C\uD574\uD55C \uC778\uC2A4\uD134\uC2A4(instance)\uAC12 \uADF8\uB9AC\uACE0 \uC720\uD55C\uD55C \uC774\uC9D1\uD2B8 \uBD84\uC218\uB97C \uAD6C\uC131\uD558\uB294 \uB370\uB3C4 \uC0AC\uC6A9\uB420\uC218\uC788\uB2E4."@ko . . "Suite de Sylvester"@fr . . . . . . "\uC218\uB860\uC5D0\uC11C \uC2E4\uBCA0\uC2A4\uD130 \uC218\uC5F4(Sylvester's sequence)\uC740 \uD2B9\uC218\uD55C \uC815\uC218 \uC21C\uC11C\uC778\uB370, \uC774 \uC21C\uC11C\uC5D0\uC11C \uAC01 \uAD6C\uC131\uC6D0\uC740 \uC774\uC804 \uAD6C\uC131\uC6D0\uC73C\uB85C\uBD80\uD130\uC758 \uC0DD\uC131\uBB3C\uB85C\uC11C \uC774\uC804 \uC21C\uC11C\uC218\uC758 \uACF1\uC5D0 1\uC744 \uB354\uD55C \uC218\uC774\uB2E4. \uC2DC\uD000\uC2A4(\uC218\uC5F4)\uC758 \uCC98\uC74C \uCD9C\uD604 \uBA87 \uAC00\uC9C0 \uAD6C\uC131\uC6D0\uC778 \uD56D\uB4E4\uC740 \uB2E4\uC74C\uACFC \uAC19\uB2E4. 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 , ...... (OEIS\uC758 \uC218\uC5F4 )"@ko . "Sylvesterova posloupnost"@cs . . . "En teoria dels nombres, la seq\u00FC\u00E8ncia de Sylvester \u00E9s una seq\u00FC\u00E8ncia d'enters en qu\u00E8 cada membre de la seq\u00FC\u00E8ncia \u00E9s el producte dels membres anteriors m\u00E9s u. Els primers termes de la seq\u00FC\u00E8ncia s\u00F3n:2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (successi\u00F3 A000058 a l'OEIS)."@ca . "Sylvesters talf\u00F6ljd"@sv . . . . . "21099"^^ . "\uC2E4\uBCA0\uC2A4\uD130 \uC218\uC5F4"@ko . "In number theory, Sylvester's sequence is an integer sequence in which each term of the sequence is the product of the previous terms, plus one. The first few terms of the sequence are 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (sequence in the OEIS)."@en . . . . "D. R."@en . . . "Sylvestrova posloupnost, pojmenovan\u00E1 po Jamesovi Sylvesterovi, je matematick\u00E1 posloupnost cel\u00FDch \u010D\u00EDsel definovan\u00E1 tak, \u017Ee ka\u017Ed\u00FD prvek posloupnosti je sou\u010Dinem p\u0159edch\u00E1zej\u00EDc\u00EDch prvk\u016F plus jedna. Form\u00E1ln\u011B se definuje jako p\u0159i\u010Dem\u017E nult\u00FD \u010Dlen posloupnosti je 2, jeliko\u017E pr\u00E1zdn\u00FD sou\u010Din m\u00E1 hodnotu 1. Alternativn\u011B m\u016F\u017Ee b\u00FDt posloupnost definov\u00E1na i pomoc\u00ED kde s0 = 2."@cs . "La successione di Sylvester \u00E8 formata dai denominatori coprimi di una frazione egiziana (essa \u00E8 la somma di frazioni che hanno al numeratore l'unit\u00E0 e al denomintore numeri interi positivi distinti fra loro, per esempio 1/2+1/3. Si dimostra che ogni numero razionale positivo, a/b, pu\u00F2 essere scritto come frazione egiziana). La somma delle frazioni ottenute mettendo al denominatore i numeri della successione di Sylvester tende ad 1. I suoi primi termini sono 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 I termini della successione possono essere calcolati nel seguente modo: . Mettendo 1 come numeratore a questi numeri e sommando via via i risultati delle frazioni cos\u00EC ottenute, si ottiene una somma che converge a 1, come mostra la tabella seguente: Possiamo quindi scrivere La successione di Sylvester \u00E8 utile per ottenere approssimazioni razionali di numeri irrazionali, usando un algoritmo goloso (Algoritmo greedy, un algoritmo di ottimizzazione che procede a costruire in ciascuno dei suoi stadi successivi una soluzione ottimale locale, con la speranza di trovare la soluzione ottimale globale). Sebbene sia ovvio che i termini della sequenza di Sylvester siano coprimi, non si sa se essi siano tutti liberi da radici (tutti i termini conosciuti lo sono). Nell'insieme delle soluzioni del problema di Zn\u00E1m per una lunghezza k data, \u00E8 piacevole il fatto che almeno una delle soluzioni conterr\u00E0 i primi k - 2 numeri della sequenza di Sylvester."@it . . . . "1110821867"^^ . . . "Sylvesters talf\u00F6ljd \u00E4r en talf\u00F6ljd d\u00E4r varje tal i f\u00F6ljden \u00E4r produkten av de f\u00F6reg\u00E5ende talen plus ett, d\u00E4r det f\u00F6rsta talet \u00E4r 2. De f\u00F6rsta talen i serien \u00E4r: 2, 3, 7, 43, , , , ,... Talf\u00F6ljden \u00E4r uppkallad efter James Joseph Sylvester."@sv . . . . . . . . . . . .