幸运数

幸運數是經由類似埃拉托斯特尼篩法的演算法後留下的整數集合。埃拉托斯特尼篩法是用來產生质数的演算法，幸運數用的篩法與其類似，但是是依據整數在剩下數字數列中的位置來判斷[1]。

幸運數是在1956年在Gardiner, Lazarus、尼古拉斯·梅特罗波利斯以及斯坦尼斯瓦夫·乌拉姆所著的論文中提到了。他們在同一篇論文中也提到了另一個篩「Josephus Flavius之篩」[2]，原因是該篩法和约瑟夫斯问题的計數遊戲很類似。

幸運數的一些性質和質數類似，例如也有類似質數定理的漸近特性，有個版本的哥德巴赫猜想是針對幸運數的擴展。有無限多個幸運數。孪生素数和孪生幸運數出現的頻率也相當。不過，若Ln代表第n個幸運數，pn是第n個質數，則當n夠大時，Ln > pn[3]。

因為幸運數和質數的一些類似性質，有些數學家認為用其他的篩法也可以產出有類似性質的整數數列，不過有關此一猜想，目前還沒有足夠的理論基礎。

篩法

示明篩選幸運數過程的動畫，其中紅色的數字為幸運數。

由一組由1開始的數列為例： 

1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,...

先將所有偶數刪去，只留下奇數： 

1,    3,    5,    7,    9,   11,   13,   15,   17,   19,   21,   23,   25,...

然後把數列中的第個數字(設該數字為)的倍數对应的數刪除，即把所有第个数刪除，例如上述例子中，第數字是，所以刪去所有第個數： 

1,    3,          7,    9,         13,   15,         19,   21,         25,...

新數列的第項(每次都加上)為，因此將新數列的第個數刪除： 

1,    3,          7,    9,         13,   15,               21,         25,...

若一直重複上述的步驟，最後剩下的數就是幸運數OEIS A000959:

1、3、7、9、13、15、21、25、31、33、37、43、49、51、63、67、69、73、75、79、87、93、99......

幸运素数

幸运素数是既是素数又是幸运数的数。

最小的几个幸运素数为OEIS A031157： 3, 7, 13, 31, 37, 43, 67, 73, 79, 127……

目前猜想有無窮個幸运素数[4]。

參考資料

  1. ^ Weisstein, Eric W. Lucky Number. mathworld.wolfram.com. [2020-08-11] （英语）. 
  2. ^ Gardiner, Verna; Lazarus, R.; Metropolis, N.; Ulam, S. On certain sequences of integers defined by sieves. Mathematics Magazine. 1956, 29 (3): 117–122. ISSN 0025-570X. JSTOR 3029719. Zbl 0071.27002. doi:10.2307/3029719. 
  3. ^ Hawkins, D.; Briggs, W.E. The lucky number theorem. Mathematics Magazine. 1957, 31 (2): 81–84,277–280. ISSN 0025-570X. JSTOR 3029213. Zbl 0084.04202. doi:10.2307/3029213. 
  4. ^ Sloane, N.J.A. (编). Sequence A031157 (Numbers that are both lucky and prime). The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 

Read other articles:

Illegal (film 2010)

IllegalPoster filmSutradaraOlivier Masset-DepasseProduserJacques-Henri BronckartDitulis olehOlivier Masset-DepassePemeranAnne CoesensAlexandre GontcharovSinematograferTommaso FiorilliPenyuntingDamien KeyeuxTanggal rilis 18 Mei 2010 (2010-05-18) (Cannes) 6 Oktober 2010 (2010-10-06) (Belgia) Durasi90 menitNegaraBelgiaBahasaPrancis Illegal (Prancis: Illégalcode: fr is deprecated ) adalah sebuah film drama Belgia 2010 yang disutradarai oleh Olivier Masset-Depasse. Film tersebut...

 

زيزينيو (لاعب كرة قدم غيني بيساو)

زيزينهو معلومات شخصية الاسم الكامل José Luís Mendes Lopes الميلاد 23 سبتمبر 1992 (العمر 31 سنة)بيساو، غينيا بيساو الطول 1.76 م (5 قدم 9 1⁄2 بوصة) مركز اللعب لاعب وسط الجنسية غينيا بيساو  معلومات النادي النادي الحالي Omonia Aradippou [الإنجليزية]‏ الرقم 77 مسيرة الشباب سنوات فريق...

 

San Gabriel Mountains National Monument

National monument in the San Gabriel Mountains of California, United States San Gabriel Mountains National MonumentLocationLos Angeles County, California, United StatesCoordinates34°15′0″N 117°50′20″W / 34.25000°N 117.83889°W / 34.25000; -117.83889Area346,177 acres (140,093 ha)EstablishedOctober 10, 2014 (2014-10-10)Governing bodyU.S. Forest ServiceWebsiteSan Gabriel Mountains National Monument The San Gabriel Mountains National Mon...

Taxing and Spending Clause

Section of American Constitution Taxing and spending redirects here. For the policy, see Tax and spend. This article is part of a series onTaxation in the United States Federal taxation Alternative minimum tax Capital gains tax Corporate tax Estate tax Excise tax Gift tax Generation-skipping transfer tax Income tax Payroll tax Internal Revenue Service (IRS) Internal Revenue Code (IRC) IRS tax forms Revenue by state History Constitutional authority Taxpayer standing Court Protest Evasion Resis...

 

Doug Jones (politician)

American politician and attorney (born 1954) Doug JonesOfficial portrait, 2018United States Senatorfrom AlabamaIn officeJanuary 3, 2018 – January 3, 2021Preceded byLuther StrangeSucceeded byTommy TubervilleUnited States Attorney for the Northern District of AlabamaIn officeSeptember 8, 1997 – January 20, 2001PresidentBill ClintonPreceded byClaude Harris Jr.Succeeded byAlice Martin Personal detailsBornGordon Douglas Jones (1954-05-04) May 4, 1954 (age 69)Fairfield, A...

 

Ipeľ

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Ipeľ – news · newspapers · books · scholar · JSTOR (December 2009) (Learn how and when to remove this template message) Eipel redirects here. For the town in the Czech Republic, see Úpice. River in Slovakia and HungaryIpeľIpeľ river near ŠahyCurrent and wa...

Castelnuovo (Italie)

Cet article est une ébauche concernant une localité italienne et le Trentin-Haut-Adige. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Pour les articles homonymes, voir Castelnuovo. Castelnuovo Noms Nom allemand Neuburg Administration Pays Italie Région Trentin-Haut-Adige  Province Trentin   Code postal 38050 Code ISTAT 022049 Code cadastral C216 Préfixe tel. 0461 Démographie Population 1 08...

 

الفضل المسترشد بالله

الفضل المسترشد بالله الفضل بن أحمد بن عبد الله بن محمد بن عبد الله بن أحمد بن إسحاق بن جعفر بن أحمد بن محمد بن جعفر بن محمد بن هارون بن محمد بن عبد الله بن محمد بن علي بن عبد الله بن العباس بن عبد المطلب. تخطيط باسم الخليفة الفَضْل المُسْتَرشِد بالله معلومات شخصية الميلاد 1092 (4...

 

Buddhism in Puerto Rico

Centro Budista Padmasambhava in Santurce Part of a series onBuddhism Glossary Index Outline History Timeline The Buddha Pre-sectarian Buddhism Councils Silk Road transmission of Buddhism Decline in the Indian subcontinent Later Buddhists Buddhist modernism DharmaConcepts Four Noble Truths Noble Eightfold Path Dharma wheel Five Aggregates Impermanence Suffering Not-self Dependent Origination Middle Way Emptiness Morality Karma Rebirth Saṃsāra Cosmology Buddhist texts Buddhavacana Early Text...

Alabama nella guerra di secessione americana

Coordinate: 32°42′N 86°42′W / 32.7°N 86.7°W32.7; -86.7 Mappa dell'Alabama. Il ruolo dell'Alabama nella guerra di secessione americana fu significativo e in parte determinante. La Costituzione dell'Alabama del 1861 garantì la cittadinanza ai cittadini statunitensi al momento residenti, proibì i dazi sull'importazione di merci straniere[1], pose dei limiti all'introduzione di un esercito permanente e si oppose all'emancipazione a livello nazionale, pur soll...

 

Banua Niha Keriso Protestan

Banua Niha Keriso ProtestanLogo BNKPPenggolonganProtestan, LutheranPemimpinEphorus Pdt. Otoriteit Dachi, S.Th., M.SiWilayahIndonesiaDidirikan1936 Nias, Sumatera UtaraUmat688.800 jiwaSitus web resmihttp://turiabnkp.orgE-mail: [email protected]; [email protected] Gereja BNKP di Kota Tebing Tinggi Banua Niha Keriso Protestan (disingkat BNKP) adalah sebuah kelompok Gereja Kristen Protestan denominasi Lutheran, yang ada di Pulau Nias, Sumatera Utara. Kantor Pusat Sinode BNKP berada di Jl. S...

 

2013–14 Arizona State Sun Devils men's basketball team

American college basketball season 2013–14 Arizona State Sun Devils men's basketballNCAA tournament, round of 64ConferencePac-12 ConferenceRecord21–12 (10–8 Pac-12)Head coachHerb Sendek (8th season)Assistant coaches Dedrique Taylor Eric Musselman Larry Greer Home arenaWells Fargo ArenaSeasons← 2012–132014–15 → 2013–14 Pac-12 Conferencemen's basketball standings Conf Overall Team W   L   PCT W   L   PCT No. 4 Arizona 15 – 3 ...

Western sports

Sports associated with Western cultureFor the sports associated with the Western United States, see Western sports (North America).A depiction of the FIFA World Cup, the most popular sporting event in the world. Western sports are sports that are strongly associated with the West.[a] Many modern sports were invented in or standardized by Western countries;[1] in particular, many major sports were invented in the United Kingdom after the Industrial Revolution,[2][3&...

 

Магнитное поле Земли

Обтекание магнитосферы Земли солнечным ветром Магни́тное по́ле Земли́ или геомагни́тное по́ле — магнитное поле, генерируемое внутриземными источниками. Предмет изучения геомагнетизма. Появилось 4,2 млрд лет назад[1]. Содержание 1 Строение и характеристики маг�...

 

Swing state

Term for any American state where neither party's candidate for election has overwhelming support Map of states by margin in the 2020 United States presidential election, relative to the national popular vote margin (4.5% in favor of Biden).Map Legend:  Partisan lean of under 5 points toward the Democratic presidential nominee (Incumbent president Joe Biden)   Partisan lean of under 5 points toward the Republican presidential nominee (former president Donald Trump)  &...

浙江民泰商业银行

此條目没有列出任何参考或来源。 (2019年1月6日)維基百科所有的內容都應該可供查證。请协助補充可靠来源以改善这篇条目。无法查证的內容可能會因為異議提出而被移除。 浙江民泰商业银行股份有限公司Zhejiang Mintai Commercial Bank Co., Ltd.簡稱浙江民泰商业银行、民泰银行、MTB支付系統行號总行：313345400010总行营业部：313345400028金融許可證機構編碼B0161H233100001统一社会信用代�...

 

Swalwell

This article is about the village in England. For the hamlet in Alberta, Canada, see Swalwell, Alberta. For people with the surname, see Swalwell (surname). Human settlement in EnglandSwalwellSwalwellLocation within Tyne and WearPopulation3,200 (2001)OS grid referenceNZ203622Metropolitan boroughGatesheadMetropolitan countyTyne and WearRegionNorth EastCountryEnglandSovereign stateUnited KingdomPost townNEWCASTLE UPON TYNEPostcode districtNE16Dialling cod...

 

إينوكيتي أنينسكي

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (مارس 2018) إينوكيتي أنينسكي   معلومات شخصية الميلاد 20 أغسطس 1855 [1][2]  أومسك[1]  الوفاة 30 نوفمبر 1909 (54 سنة) [1][2]  سانت بطرسبرغ[1]  سبب الوف�...

Nanteuil-la-Fosse

Cet article est une ébauche concernant une commune de l’Aisne. Vous pouvez partager vos connaissances en l’améliorant (comment ?). Le bandeau {{ébauche}} peut être enlevé et l’article évalué comme étant au stade « Bon début » quand il comporte assez de renseignements encyclopédiques concernant la commune. Si vous avez un doute, l’atelier de lecture du projet Communes de France est à votre disposition pour vous aider. Consultez également la page d’aide �...

 

Роулинсон, Генри Кресвик

В Википедии есть статьи о других людях с такой фамилией, см. Роулинсон; Роулинсон, Генри. Генри Роулинсонангл. Henry Rawlinson Парадный фотопортрет 1865 года Дата рождения 10 апреля 1810(1810-04-10) Место рождения Чадлингтон[англ.], Оксфордшир Дата смерти 5 марта 1895(1895-03-05) (84 года) Ме�...