61. Knuth: Recent News Øystein Ore, 18991968, who was a student of; Thoralf Albert Skolem, 18871963,who was a student of; axel thue, 18631922, who was a student of http://www-cs-faculty.stanford.edu/~knuth/news02.html

Recent News [click here to zip down to the schedule of public lectures] 1000000 Years Old! I got a bit older at the beginning of this year ... and, wow, what a wonderful surprise celebration we had! I can't sufficiently thank all my friends who traveled to Stanford and treated me to some of the absolutely most thrilling days of my life, as we celebrated the joys of Computer Science in general and Analysis of Algorithms in particular. Great talks by Persi Diaconis, Scott Kim, Bob Sedgewick, Philippe Flajolet, Svante Janson, Jeff Vitter, Andrei Broder, Andrew Odlyzko, Herb Wilf, Bob Tarjan, Leo Guibas, and Vaughan Pratt - plus a great organ concert by Gwen Adams and Joseph Hansen - and a chance to greet more than a hundred people that I rarely get to see, including more than twenty of the students whose dissertations I've had the good fortune to sign in years past. Thank you all enormously for a festive event that will live forever in my memory. It could not have been more perfect! Farewell, Mom memorial booklet that celebrates her life and work.

62. Thue - 1897 Translate this page axel thue - 1897. thue benutzt in seinem Beweis den Hauptsatz der Zahlentheorie,also die Eindeutigkeit der Zerlegung der natürlichen Zahlen in ihre http://www.mathematic.de/beweise/primenumbers-thue.html

Axel Thue - 1897 Seien n und k Weiterhin seien nun alle Primzahlen, die m mit Dabei ist Wird nun ist. Es gibt also mindestens k+1 Primzahlen p mit Wird k Paulo Ribenboim, The Book of Prime Number Records, Springer-Verlag 1989, 2. Auflage www.mathematic.de

63. Mathematics Of Computation A. thue, Et par antydninger til en taltheorisk methode, Selected MathematicalPapers of axel thue, Universitetsforlaget, Oslo 1977. MR 5746 http://www.ams.org/mcom/2002-71-239/S0025-5718-01-01381-3/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6842(e) ISSN 0025-5718(p) Previous issue Table of contents Next issue Articles in press ... All issues Thue's theorem and the diophantine equation Author(s): Keith Matthews. Journal: Math. Comp. MSC (2000): Primary 11D09 Posted: September 17, 2001 Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: A constructive version of a theorem of Thue is used to provide representations of certain integers as , where References: J. Brillhart, Note on representing a prime as a sum of two squares , Math. Comp. MR G. Cornacchia, Su di un metodo per la risoluzione in numeri interi dell' equazione , Giornale di Matematiche di Battaglini K. Hardy, J.B. Muskat, K.S. Williams, A deterministic algorithm for solving in coprime integers and , Math. Comp. MR K. Hardy, J.B. Muskat, K.S. Williams, Solving using the Euclidean algorithm , Utilitas Math.

64. Axel Thue Université Montpellier II Translate this page axel thue (1863-1922). Cette image et la biographie complète en anglais résidentsur le site de l’université de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1897

65. Matematisk Vekst I Abels Fotspor Også axel thue, Thoralf Skolem, Viggo Brun, Ernst Selmer, Vilhelm Ljunggren og ikke axel thue arbeidet med tallteori, logikk, geometri og mekanikk. http://www.forskning.no/Artikler/2002/juni/1023116423.71

gå til forsiden abonner på nyhetsbrev kontakt oss les om forskning.no ... Naturvitenskap i fokus Abelprisen Abelprisen tildelt Peter Lax Abelfondets profil Abels matematikk ... Niels Henrik Abel (1802–1829) forskning.no Sagveien 23b Pb. 2070 Grünerløkka 0505 OSLO tel 22 80 98 90 fax 22 80 98 99 epost@forskning.no Ansvarlig redaktør: Steinar Q. Andersen Faglig redaktør: Erik Tunstad Medlemmer i forskning.no: Høgskolen i Bergen Høgskolen i Bodø Høgskolen i Lillehammer Høgskolen i Oslo ... Veterinærinstituttet forskning.no har mottatt Merket for God Design i samarbeid med Creuna AS. forskning.no vant den nasjonale konkurransen i World Summit Award 2005. Matematisk vekst i Abels fotspor 04.jun 2002 07:00 Av: Bjarne Røsjø , Informasjonsrådgiver Niels Henrik Abel er ett av de største matematiske genier verden har fostret, og årets 200-årsjubileum brukes til å markere hans innsats. Det er ikke fullt så godt kjent at det grodde friskt i sporene etter Abel så godt at Norge nærmest var en matematisk stormakt på slutten av 1800-tallet og langt utover på 1900-tallet. - Du skal ikke åpne mange lærebøker i avansert matematikk før du støter på Axel Thues teorem, Sophus Lies grupper eller Ludwig Sylows teorier. Norge som nasjon var overrepresentert med fremragende matematikere på slutten av 1800-tallet, forteller Geir Ellingsrud, som er professor i matematikk ved UiO og deltaker i årets forskningsgruppe i matematikk ved SHS.

66. Norske Matematikere Selected Mathematical Papers of axel thue. Universitetsforlaget, Oslo 1977.Sigmund Selberg axel thue. Normat 28 (4) (1980) pp. 133 144. http://home.hia.no/~aasvaldl/norskem.html

Norske matematikere Navigasjonslinker: Min hjemmeside. Norske matematikere Adresser til norske matematikere Bent Birkeland har samlet en del materiale i "Norske matematikere". Gyldendal Norsk Forlag Professorer i matematikk ved Universitetet i Oslo. Tapir Avdeling for realfag, hjemmeside. Niels Henrik Abel (1802 - 1829) ABELSENTERET i Gjerstad "Niels Henrik Abel - et geni og hans samtid" . Gyldendal Norsk Forlag, Oslo (1954). "Niels Henrik Abel: mathematician extraordinary." University of Minnisota Press (1957). de Niels Henrik Abel. - Nouv. ed. Johnson Reprint Corporation (1965). Bilder og kart (kommer ...). Fr. Lange-Nielsen: "Niels Henrik Abel." Nordisk Mat. Tidsskrift. Bd. 1 (1953) pp. 65 - 90. Karl Egil Aubert: "Niels Henrik Abel." Normat nr. 27 (4) (1979) pp. 129 - 140. Aschehoug forlag Et foranskutt lyn: Niels Henrik Abel og hans samtid Oversettelse til engelsk Springer-Verlag , se anmeldelse av Jeremy J. Gray i MAA Online Arild Stubhaug: " Abelhaugen i Slottsparken." Kronikk i Aftenposten, 25.09.96. Niels Henrik Abel side ved MacTutor History of Mathematicians archive.

67. Bees While this may seem obvious , it was proved only in the late nineteenth centuryby the Norwegian mathematician axel thue. What is obvious, is that the http://www.pims.math.ca/education/2000/bus00/bees/

The Pacific Institute for the Mathematical Sciences launched a new web site on March 31, 2005. If there is any discrepancy between the information on this page and the new site, the information on the new site should be used. Packings. If 4% of the distance between cell centres is wax, how much of the total surface is wax? Further down on this page, you'll get a chance to submit your answer. The surface of the honeycomb is tightly covered by hexagonal "nuts" like the one shown on the right (not quite to scale), in which the yellow and red represent wax and the blue line marks half the distance between cell centres. If you wish to cover the entire plane with identical circular discs (e.g., pennies) in the densest possible way, you cannot do better than the bees. While this may seem "obvious", it was proved only in the late nineteenth century by the Norwegian mathematician Axel Thue. What is obvious, is that the planar "kissing number" is 6: exactly six pennies can be laid around a single central one; what is not too difficult to prove, is that the honeycomb presents the most efficient lattice (i.e., regular) packing of pennies in a plane. The hard part is to show that this cannot be improved by some clever irregular scheme. If you restrict yourself to a finite part of the plane, the problem does not become easier, but much

68. Citebase - A Generalization Of Repetition Threshold axel thue s Papers on Repetitions in Wordsa Translation. Reprinted in SelectedMathematical Papers of axel thue, T. Nagell, editor, http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:math/0310144

69. Citebase - Polynomial Versus Exponential Growth In Repetition-Free Binary Words Reprinted in Selected Mathematical Papers of axel thue, T. Nagell, editor,Universitetsforlaget, Oslo, 1977, pp. 139158. http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:math/0304095

70. S. Arshon Demonstration De L Existence Des Suites Asymetriques (Russian) 7872 Jean Berstel axel thue s work on repetitions in words. axel thue Ueber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. http://felix.unife.it/Root/d-Mathematics/d-Dynamical-systems/d-Topological-dynam

S. Arshon: Demonstration de l'existence des suites asymetriques infinies. Mat. Sb. 44 (1937), 769-777. (Russian) 7872 Jean Berstel: Axel Thue's work on repetitions in words. Internet 1995, 16p. Valerie Berthe'/Sebastien Ferenczi/Christian Mauduit (ed.): Substitutions in dynamics, arithmetics and aombinatorics. Springer LN Math. 1794 (2002), 400p. Eur 63. The volume is published under the pseudonym N. Pytheas Fogg (why ?). Ethan Coven: Endomorphisms of substitution minimal sets. Zeitschr. Wtheorie 20 (1971), 129-133. 10478 Ethan Coven/Michael Keane: The structure of substition minimal sets. Trans. AMS 162 (1971), 89-102. 10518 F. Dekking: The spectrum of dynamical systems arising from substitutions of constant length. Z. Wtheorie 41 (1978), 221-239. 10573 F. Dekking/Michael Keane: Mixing properties of substitutions. Z. Wtheorie 42 (1978), 23-33. Aldo De Luca/Stefano Varricchio: Some combinatorial properties of the Thue-Morse sequence and a problem in semigroups. Theor. Comp. Sci. 63 (1989), 333-348. 15419 Andrew Gleason: Semigroups of shift register matrices. Math. Systems Theory 25 (1992), 253-267. From a course given at Princeton in 1960. 7902 Walter Helbig Gottschalk: Substitution minimal sets. Trans. AMS 109 (1963), 467-491. 1031 Walter Helbig Gottschalk/Gustav Arnold Hedlund: Topological dynamics. AMS 1955. 2554 Walter Helbig Gottschalk/Gustav Arnold Hedlund: A characterization of the Morse minimal set. Proc. AMS 15 (1964), 70-74. 10516 Gustav Arnold Hedlund: Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320-375. 14037 Charles Holton/Luca Zamboni: Geometric realizations of substitutions. Bull. Soc. Math. France 126 (1998), 149-179. 12126 Teturo Kamae: Spectrum of a substitution minimal set. J. Math. Soc. Japan 22 (1970), 567-578. 2555 Michael Keane: Generalized Morse sequences. Zeit. Wtheorie 10 (1968), 335-353. 5716 Harvey Keynes: The proximal relation in a class of substitution minimal sets. Math. Systems Theory 1 (1967), 165-174. 10479 Nelson Markley: Substition-like minimal sets. Israel J. Math. 22 (1975), 332-353. 830 John Martin: Substitution minimal flows. Am. J. Math. 93 (1971), 503-526. 10512 John Martin: Minimal flows arising from substitutions on non-constant length. Math. Systems Th. 7 (1973), 73-82. 10517 John Martin: Generalized Morse sequences in n symbols. Proc. AMS 54 (1976), 379-383. 10519 John Martin: The structure of generalized Morse minimal sets on n symbols. Trans. AMS 232 (1977), 343-356. P. Michel: Stricte ergodicite' d'ensembles minimaux de substitutions. C.R. Ac. Sci. Paris 278 (1974), 811-813. Marston Morse: Recurrent geodesics on a surface of negative curvature. Trans. AMS 22 (1921), 84-100. Marston Morse: A solution of the problem of infinite play in chess. Abstract 360, Bull. AMS 44 (1938), 632. Marston Morse/Gustav Arnold Hedlund: Unending chess, symbolic dynamics and a problem in semigroups. Duke Math. J. 11 (1944), 1-7. G. Rauzy: Nombres algebriques et substitutions. Bull. Soc. Math. 110 (1982), 147-178. Axel Thue: Ueber unendliche Zeichenreihen. Norske Vid. Selsk. Skr. (?) 7 (1906), 1-22. Axel Thue: Ueber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Videnskabsselskabets Skrifter (?) (1906), ... Axel Thue: Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. (?) 1 (1912), 1-67.

71. Molte Figure Che Compaiono In Questa Applet Sono Grandi E Tendono Translate this page Il matematico axel thue (1863-1922) si chiese se esista una sequenza infinitabinaria (fatta di 0 e 1) nella quale non appaiano mai 2 blocchi consecutivi di http://alpha01.dm.unito.it/personalpages/cerruti/Az1/thue.html

Se non le conoscete leggete le istruzioni Thue Azionando l'applet (che conviene rimpicciolire) partono 4 trenini nelle 4 direzioni, producendo degli alianti che collidono. Quello che ci interessa sono le 4 sequenze diagonali di semafori che si leggono partendo dal centro. Il centro è vuoto e la successione comincia con 0; seguono 1 1, cioè vi sono 2 semafori uno di seguito all'altro, poi vi è uno spazio vuoto che leggiamo come 0, poi 1 1 e così via. L'inizio della successione è il seguente: 0110110111110110111110110110... Questa successione è definita in modo ricorsivo, in maniera simile alla famosa successione di Prouhet-Thue-Morse. Il matematico Axel Thue (1863-1922) si chiese se esista una sequenza infinita binaria (fatta di e 1) nella quale non appaiano mai 2 blocchi consecutivi di 3 simboli uguali nè blocchi della forma awawa dove a è od 1 e w un arbitrario blocco binario. In effetti esiste, e comincia così: 0110100110010110100101100110... Essa può essere definita formalmente in molti modi; ne vediamo due. Nel seguito dato un bit t denotiamo con t' il suo complemento : t'=0 se t=1, t'=1 se t=0.

72. Biografisk Register Translate this page thue, axel (1863-1922) Torricelli, Evengelista (1608-47) Tsjebysjev, PafnutijLvovitsj (1821-94) Turing, Alan M. (1912-54) Unguru, Sabetai http://www.geocities.com/CapeCanaveral/Hangar/3736/biografi.htm

Biografisk register Matematikerne er ordnet alfabetisk på bakgrunn av etternavn. Linker angir at personen har en egen artikkel her. Fødsels- og dødsår oppgis der dette har vært tilgjengelig. Abel, Niels Henrik Abu Kamil (ca. 850-930) Ackermann, Wilhelm (1896-1962) Adelard fra Bath (1075-1160) Agnesi, Maria G. (1718-99) al-Karaji (rundt 1000) al-Khwarizmi, Abu Abd-Allah Ibn Musa (ca. 790-850) Anaximander (610-547 f.Kr.) Apollonis fra Perga (ca. 262-190 f.Kr.) Appel, Kenneth Archytas fra Taras (ca. 428-350 f.Kr.) Argand, Jean Robert (1768-1822) Aristoteles (384-322 f.Kr.) Arkimedes (287-212 f.Kr.) Arnauld, Antoine (1612-94) Aryabhata (476-550) Aschbacher, Michael Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Ball, Walter W. R. (1892-1945) Banach, Stéfan (1892-1945) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Bharati Krsna Tirthaji, Sri (1884-1960)

73. Ny Side 1 thue, axel (1863-1922) Torricelli, Evengelista (1608-47) Zenon (ca. http://www.matte.no/matematikere.htm

Kurs i Matematikkens kulturhistorie. Siden er under arbeid - sist oppdatert Indexes of Biographies Abel, Nils Henrik Abelsenteret Matematikkens verden Om NHA Mat. kulturhist. Arkimedes Matematikkens verden Ackermann, Wilhelm (1896-1962) Aristoteles (384-322 f.Kr.) Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Binet, Jacques Philippe Marie (1786-1856) Boole, George (1815-64) Brahe, Tyco (1546-1601) Brun, Viggo (1885-1978) Cayley, Arthur (1821-95) Ceva, Giovanni (1647-1734) Chatelet, Gabrielle-Émilie de (1706-49) Chhin Chiu-Shao (1202-61) Chu Shih-Chieh (ca. 1270-1330)) Chuquet, Nicolas (1445-88) Cohen, Paul J. (1934-) Cole, Frank Nelson (1861-1926) Comandino, Federigo (1506-1575)

74. Juristforeningen.no axel thue. Arvid Frithjof Rasmussen. 1927, Knut Tvedt. 1926, Birger Motzfeld.John Lyng. 1925, Jørgen SindingLarsen. Thomas Thorsen. Christian Kaurin http://www.juristforeningen.no/jf/ordenskollegiet_dekorandi.html

Til forsiden Om Juristforeningen Kontakt oss Formannskapet ... Stud.Jur. Dekorandi i Juristforeningen Riddere av Den gyldne paragraf År Navn Devise Johan Christian Kongsli Ane Smestad Torkildsen Olav Magnus Moen Cable guy. Andreas Langerud Nesheim Audun Hellner Humakstyrets stolte ganger, svenska flickor, bondeanger. Pål Osmundsen Kongedass og machomann, krydrer Bærums drikkevann. Kari Steig Cabaret-blondine, busy-bee, JVL-sjef uten ski. Jens Christian Gjesti Karate Kid og småsjarmør, pusekatt med klipte klør. Kirsten Borge Alle gode ting er tre, men to er heller ikke å forakte. Audun Halvorsen Hoppens yngste bestefar, avmålt tunge, sindig svar Nina Fladsrud Jurkemerra fikk momssperra Jarran Dolve Full, gass, tiss, tass Lars-Jørgen Kihlberg Olsen Kleptokanari Dag Vemund Haanæs Sminkepung og unge piker, koker suppe på en spiker

75. Program : PATSOFT Konferansen Foredragsholdere Tom Ekeberg, Haakon thue Lie og axel Moulin (Leogriff).Skriving av patentsøknader bør overlates til erfarne patentrådgivere. http://www.patsoft.no/program.php

om PATsoft Forsiden Program Foredragsholdere ... Hvorfor Program onsdag 11. mai format. Tid Innhold Registrering / kaffe og te Velkommen ved konferansier Eva Bratholm Kaj Arnö, Vice President MySQL AB Revenue models and IPR strategies for Open source software Bjørn Olstad, CTO Fast Search and Transfer ASA Salget av Fasts søkemotor ”All the web” til amerikanske Overture var en suksess - Fast innkasserte over 500 mio NOK på salget. Hva slags forretningsmodell /IPR hadde Fast? Hvilken rolle spilte Fasts patenter/IPR tilknyttet søketeknologien i salget? Hva lærte Fast av dette, hva kan andre teknologibedrifter lære? Pause, kaffe og te Jon Bing, professor Historisk bakteppe for fremveksten av patent på programvare - hvorfor er vi der vi er i dag? Hva bør vi vite om de ulike beskyttelsesregimer (herunder patent og opphavsrett)? Tom Ekeberg: IPR og valg av forretningsmodeller Relasjonen mellom forretningsmodeller og IPR - hvorfor er IPR viktig? Hvordan etablere IPR for programvare? Hvordan påvirker IPR utforming av forretningsmodellen og visa versus? Fordeler/ulemper med patentering av programvare Lunsj Eirik Chambe-Eng, President and co-founder Trolltech AS

76. Skaff Deg En IPR-strategi! - Teknisk Ukeblad HOLD PÅ HEMMELIGHETENE Ikke la konkurentene dine får nyss om dine oppfinnelser.Haakon thue Lie og axel Moulin ber bedrifter om å velge en klar strategi. http://www.tu.no/nyheter/samfunn/article35721.ece

Hovedside Søk i nyhetsarkiv Avansert søk Nyheter Sudoku NY! Orkanen NY! Arbeidsliv - Utdanning Bygg - Anlegg Energi - Elektro Forsvar ... Mattenøtter Tema Eliaden 2004 150 år Statsbudsjettet 2004 Elkraft Energi ... Sudoku NY! Orkanen NY! Arbeidsliv Bygg Energi Industri ... Annonsere? Stillingskode Guider Levert av BizKit Anbudsguiden Annonseinfo Bedriftshjelperen Jobbsøkerguiden ... Våre Veger Ut i verden Søk i Google Søk i Fast TEKNA NITO PF Papirutgaven Les siste utgave Arkiv (PDF) Mediaplan TU 2005 Annonseinfo Du er her: tu.no Nyheter Samfunn - Politikk Snarveier Anbudsguide Jobb Møtekalender Annonseinfo ... Stresstest Skaff deg en IPR-strategi! Ragna Kronstad Publisert: 13.05.2005 13:05 Holder bedriften din godt nok på hemmelighetene? Vet ledelsen hva de ansatte sitter på av kunnskap? Har dere en oversikt over hvilke patenter dine konkurrenter søker på? Er du litt usikker på disse spørsmålene, kan det hende bedriften din mangler en helheltlig IPR- strategi. HOLD PÅ HEMMELIGHETENE: Ikke la konkurentene dine får nyss om dine oppfinnelser. Haakon Thue Lie og Axel Moulin ber bedrifter om å velge en klar strategi. Foto: RAGNA KRONSTAD Gode råd *Forstå betydningen av IPR. Evaluer risiko og muligheter.

77. Thue http://serge.mehl.free.fr/chrono/Thue.html

théorie des nombres). Crelle (1909) concernant la recherche des points à coordonnées entières sur une courbe algébrique : + y + y Cette . Le mathématicien anglais Alan Baker apporta des précisions (1968) sur le théorème de Thue en précisant une borne supérieure des x et y. Mordell Siegel Un t héorème de Thue sur l'approximation rationnelle des nombres algébriques : Pour en savoir plus : Ed. Hermann - 1978, 1992 Fields Young

78. Cat's Eye Technologies: /projects/thue/ (and possibly created by) the Norwegian mathematician Axelthue (pronounced \ TOOay\ ). thue represents one of the simplest possible waysto construe http://catseye.mine.nu:8080/projects/thue/

Projects Erlang Perl Esolangs ... Vintage The Thue Programming Language Conceived and implemented by John Colagioia For want of a nail, the shoe was lost. For want of a shoe, the horse was lost. For want of a horse, the knight was lost. For want of a knight, the battle was lost. So it was a kingdom was lost, all for the want of a nail. George Herbert, Jacula Prudentum (Colloqual Adaptation) The Thue programming language was invented by John Colagioia in early 2000. It is named after the computational regimen it is based on - a pure string-rewriting process called a semi-Thue grammar Thue represents one of the simplest possible ways to construe constraint-based programming. It is to the constraint-based paradigm what languages like OISC are to the imperative paradigm; in other words, it's a tar pit. Project Branch Path Rev thue current Rev File Size Date Keywords Description archive/ doc/ eg/ src/

79. PlanetMath: Prouhet-Thue-Morse Sequence History. The thueMorse sequence was independently discovered by P. Prouhet, Axelthue, and Marston Morse, and has since been rediscovered by many others. http://planetmath.org/encyclopedia/ProuhetThueMorseSequence.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Prouhet-Thue-Morse sequence (Definition) The Prouhet-Thue-Morse sequence is a binary sequence which begins as follows: The th term is defined to be the number of s in the binary expansion of , modulo 2. That is, if the number of s in the binary expansion of is even, and if it is odd The sequence satifies the following recurrence relation , with The Prouhet-Thue-Morse sequence is an automatic sequence. It has been shown to be cube-free and overlap-free when viewed as a word of infinite length over the binary alphabet Generating function The generating function for the sequence satifies the relation History The Thue-Morse sequence was independently discovered by P. Prouhet, Axel Thue, and Marston Morse, and has since been rediscovered by many others. References Allouche, J.-P.; Shallit, J. O.

80. Formal Numbers This site is dedicated to the memory of the norwegian mathematician AxelThue (18661922), who proved one of the most remarkable result of the twentieth http://www.math.u-bordeaux.fr/~lasjauni/

FORMAL NUMBERS by Alain Lasjaunias Alain.Lasjaunias@math.u-bordeaux1.fr Publications and also for a more academic text A short survey on diophantine approximation in fields of formal numbers Click here to enter... This site is dedicated to the memory of the norwegian mathematician Axel Thue (1866-1922), who proved one of the most remarkable result of the twentieth century in number theory Our goal is to present in an elementary way a class of abstract numbers . These numbers have been progressively introduced and studied in the last fifty years. Unlike real numbers, they are of no use to measure physical quantities but will certainly have applications still unknown. The further removed from usefulness or practical application, the more important. Axel Thue

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