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Topic: The Online Encyclopedia of Integer Sequences

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	Integer sequence - Wikipedia, the free encyclopedia
		An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms.
		The set of computable integer sequences and definable integer sequences are both countable, with the computable sequences a proper subset of the definable sequences.
		The set of all integer sequences is uncountable; thus, almost all integer sequences are uncomputable and cannot be defined.
	en.wikipedia.org /wiki/Integer_sequence (229 words)

	On-Line Encyclopedia of Integer Sequences - Wikipedia, the free encyclopedia
		Any sequence with this keyword ought to be cross-referenced to its matching sequence of numerators or denominators, though this may be dispensed with for sequences of Egyptian fractions, such as A069257, where the sequence of numerators would be A000012.
		If a sequence has the keyword "full," it should also have the keyword "fini." One example of a finite sequence given in full is that of the supersingular primes A002267, of which there are precisely fifteen.
		Sequence A073502, the magic constant for n X n magic square with prime entries (regarding 1 as a prime) with smallest row sums, is an example of a sequence with offset 3, and A072171, "Number of stars of visual magnitude n." is an example of a sequence with offset -1.
	en.wikipedia.org /wiki/On-Line_Encyclopedia_of_Integer_Sequences (4425 words)

	Encyclopedias Online (Site not responding. Last check: 2007-11-04)
		De Imperatoribus Romanis: An Online Encyclopedia of Roman Emperors - DIR is an on-line encyclopedia on the rulers of the Roman empire from Augustus (27 BC-AD 14) to Constantine XI Palaeologus (1449-1453).
		Encyclopedia of the Orient - An outstanding encyclopedia of North Africa and the Middle East.
		Encyclopedia of Macedonian History 2000 - The program includes the History of Macedonia from the times of Phillip II of Macedon and Alexander the Great, to year 2000 and the last Presidential Elections in Macedonia.
	www.ehhs.cmich.edu /tepd/pdsite/curriculum/searching/encyc.html (2781 words)

	Integer Sequences
		This very simple sequence is in the Encyclopedia as A000290.
		This sequence is n(n+3)/2, at A000096, where it is given starting at zero.
		Clearly, there is little new in these geometric integers, but other sequences can be derived by combinations of functions from the two groups.
	www.comp.utas.edu.au /users/nholmes/sqncs (520 words)

	Integer sequence Information - TextSheet.com (Site not responding. Last check: 2007-11-04)
		An integer sequence may be specified explicitly by giving a formula for its n-th term, or implicitly by giving a relationship between its terms.
		(the Fibonacci sequence) is formed by starting with two ones and then adding any two consecutive terms to obtain the next one: an implicit description.
		Information about thousands of integer sequences is recorded in Neil Sloane's Encyclopedia of Integer Sequences, online at." class="external">http://www.research.att.com/~njas/sequences/.
	sparrow.sferahost.com /encyclopedia/i/in/integer_sequence.html (123 words)

	The South End Newspaper - Mathematician reaches 100k milestone for online integer archive - NATION/WORLD - News (Site not responding. Last check: 2007-11-04)
		There are sequences in the OEIS that relate to physics — such as the centered cube numbers that relate to shells of atoms — biology and even music (such as 2, 2, 4, 4, 2, 6, 6, 2, 8, 8, 16, which is in the lyrics of an Argentine children’s song).
		Sloane started rounding up integer sequences in the 1960s, entering them on punch cards, when he was working on neural networks as a graduate student at Cornell University.
		Although Sloane acknowledges that all the “core” sequences — such as the prime numbers, Catalan numbers, and the Fibonacci sequence — are already in the database, he believes the OEIS has an infinite potential for expansion.
	www.southend.wayne.edu /modules/news/article.php?storyid=553 (1217 words)

	Math Trek: The EKG Sequence, Science News Online, April 6, 2002 (Site not responding. Last check: 2007-11-04)
		Many people are familiar with the Fibonacci sequence, in which each new term is the sum of the previous two terms: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on.
		The sequence was discovered last year by Jonathan Ayres, and it now appears as entry A064413 in Sloane's encyclopedia.
		For instance, whenever a prime p occurs in the sequence, it is preceded by 2p and followed by 3p.
	www.sciencenews.org /articles/20020406/mathtrek.asp (559 words)

	SEQUENCES
		The sequence may be finite or infinite, reveal a pattern or appear entirely random.
		First we should note that in mathematical circles the formal definition of a sequence is commonly cast in the form of a function.
		The Length of the Hailstone sequence is the number of terms in the sequence until the subsequence 4, 2, 1 appears.
	isolatium.uhh.hawaii.edu /m206L/lab9/sequences/sequences.htm (903 words)

	OEIS [Definition] (Site not responding. Last check: 2007-11-04)
		The On-Line Encyclopedia of Integer Sequences (OEIS) is a web-based searchable databaseA database is an information set with a regular structure.
		It is considered one of the major resources in mathematicsMathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers".
		The database contains over 100000 sequences as of November 20042004 was a leap year starting on Thursday of the Gregorian calendar.
	www.wikimirror.com /OEIS (1056 words)

	On-Line Encyclopedia of Integer Sequences - free-definition (Site not responding. Last check: 2007-11-04)
		The Encyclopedia is a database recording information on integer sequences that are of interest in mathematics.
		The database contains over 93000 sequences as of April 2004.
		As a spin-off from the database work, Sloane founded the Journal of Integer Sequences (http://www.math.uwaterloo.ca/JIS/) in 1998.
	www.free-definition.com /On-Line-Encyclopedia-of-Integer-Sequences.html (374 words)

	Welcome to the On-Line Encyclopedia of Integer Sequences
		If your sequence isn't in the database, and if it is interesting, please submit it using the web page for contributing a new sequence or comment.
		Most of the sequences are arranged in the database in lexicographic order of absolute values, indexed by the position of the first term that is greater than 1 in absolute value.
		Sequences that contain only 0's, 1's and -1's are in strict lexicographic order by absolute value at the beginning of the table.
	www.research.att.com /~njas/sequences/Seis.html (1691 words)

	SIAM Review of ``An Encyclopedia of Integer Sequences'' by N. J. A. Sloane & Simon Plouffe
		The idea is that a researcher who encounters a sequence in her or his work, and wishes to quickly find out what is known about the sequence (does it have a name, for example, such as ``the Euler numbers'' or ``the Stirling numbers of the first kind''?), can look it up here.
		Some of the heuristics discussed in chapters 1, 2, and 3 (before the table of sequences proper begins) give useful hints as to what to do when the computer programs don't work; they also give a nice conceptual model of the inner workings of the programs.
		Further, about 25% of the sequences in the book are obtained from a rational generating function or elementary manipulation thereof (reversion, undoing a logarithmic differentiation, etc.).
	www.cecm.sfu.ca /~jborwein/sloane/sloane.html (630 words)

	Math Games: Integer Complexity
		Out of the first 150000 numbers, the two sequences require the same number of 1's 54000 times.
		online reference), Stephen Wolfram considered the integer complexity problem in a variety of ways.
		A056792 in the Online Encyclopedia of Integer Sequences.
	www.maa.org /editorial/mathgames/mathgames_04_12_04.html (735 words)

	Mathematical interests
		An integer sequence is simply a list of integers (which are "whole numbers," i.e.
		Some sequences are undeniably important, such as the famous Fibonacci sequence, while others are merely interesting or pretty or nifty or clever.
		See, I thought I had thought up a with a sequence to add to the encyclopedia, but it turned out someone had already thought of it.
	www.hoolehan.com /math (514 words)

	Amazon.com: Books: The Encyclopedia of Integer Sequences (Site not responding. Last check: 2007-11-04)
		The sequences arearranged in numerical order, and for each one a brief description and a reference is given.
		The number of sequences cataloged here is more than double the tally of the previous incarnation....If libraries shelve this book in the reference section, they should consider aquiring a second copy for circulation.
		Sequences are arranged lexicographically and (to minimize errors) typeset from computer tape.
	www.amazon.com /exec/obidos/tg/detail/-/0125586302?v=glance (1698 words)

	American Scientist Online - A Question of Numbers (Site not responding. Last check: 2007-11-04)
		Sloane picks the category "Integer Sequences" for $400, and Alex Trebek reads the answer: "1, 1, 2, 3, 5, 8, 13, 21...." Sloane instantly supplies the question: "What are the Fibonacci numbers?" Later it is Plouffe's turn, and he selects "Real Numbers" for $1,000.
		He is also the author of the Handbook of Integer Sequences, a compendium of some 2,300 sequences, published in 1973.
		The calculator is "inverse" in the sense that you give it a number and ask where the number might have come from, rather than giving it a formula and requesting a solution.
	americanscientist.org /template/AssetDetail/assetid/21436?&print=yes (327 words)

	Texts and tools for the Online Encylopedia of Integer Sequences (Site not responding. Last check: 2007-11-04)
		The Online Encyclopedia of Integer Sequences (OEIS) is an amazing collection with a community of SeqFans in all parts of the world.
		The special case of a sequence without signed terms marked as sign but not nonn is only reported, because the signed terms may start later, see A057752 resp.
		Various Shell sort OEIS sequences are tested: Shell's A003462, Knuth's A033622, and A055876, A055875, A036562, A036564, A036569.
	www.xyzzy.claranet.de /eis.htm (890 words)

	Assorted Encyclopedias on the Web (Site not responding. Last check: 2007-11-04)
		HinCyc: Encyclopedia of Haemophilus Influenzae Genes and Metabolism
		The Mystica: An on-line encyclopedia of the occult, mysticism, magic, paranormal and more...
		Encyclopedia of Violence, Peace, and Conflict (not on-line)
	edis.win.tue.nl /encyclop.html (63 words)

	The On-Line Encyclopedia of Integer Sequences - Sloane, On- (ResearchIndex)
		The OEIS is a database of nearly 90, 000 sequences of integers, arranged lexicographically.
		The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other information (Update)
		Sloane, The On-Line Encyclopedia of Integer Sequences, published electronically at http://www.research.att.com/¸njas/sequences/.
	citeseer.ist.psu.edu /588454.html (346 words)

	The CTK Exchange Forums (Site not responding. Last check: 2007-11-04)
		The sequence 1, 3, 17, 99, 577, , which is A001541 in the Online Encyclopedia of Integer Sequences, has some very interesting properties, some of them described in the Encyclopedia itself.
		The sum of a sequence of consecutive nonnegative integers starting with n is never a square for any n, if and only if the number of the terms in the sequence can be expressed as
		This should be amended to change "nonnegative" to positive since if i = 0 and m = 25 there are in fact solutions to m consecutive positive integers summing to a square.
	www.cut-the-knot.com /htdocs/dcforum/DCForumID4/614.shtml (606 words)

	Bubble Chamber: November 2000 Archives (Site not responding. Last check: 2007-11-04)
		Fueled by adenosine triphosphate (ATP, the so-called energy of cellular life) and able to spin nickel propellers at eight revolutions per second, these molecular motors made of ATPase enzyme are said to herald a new generation of ultrasmall, robotic devices.
		His goal is to have all interesting number sequences in the table.
		Some sequences come with an entreaty: "More terms please," so if you have an idle computer (or hundreds of them), you can help build the database.
	bc.tensegrity.net /archives/2000_11.html (460 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		It says that the first element of seq is the (firstindex)th term of the sequence as defined in the Name or Ref or Formula, etc...
		In the description, a(n) usually denotes the n-th term of the sequence, \ and n is a typical subscript.
		The %R line is used mostly in the older sequences that are in the book, or for sequences in the most common journals.
	www.ccr.jussieu.fr /gmpib/seqfan/EISFormat.m (1178 words)

	On-Line Encyclopedia of Integer Sequences - Sloane, On- (ResearchIndex)
		Storage space is no longer a problem, and the data-base has grown to more than 10 times the size of the 1995 book.
		The programmable version of vi, ex, is extensively used in processing sequences.
		The graph only includes citing articles where the year of publication is known.
	citeseer.ist.psu.edu /233442.html (255 words)

	Ed Pegg's Math Games - Sequence Pictures
		Here are the whole numbers / natural numbers / positive integers up to 700, in binary columns.
		In Stephen Wolfram's book A New Kind of Science, many sequence pictures can be found in Chapter 4.
		A000001, A000005, A000027, A000040, A000043, A000045, A000056, A000217, A000290, A000578, A001203, A001299, A003188, A007318 in "The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/.
	www.maa.org /editorial/mathgames/mathgames_12_08_03.html (451 words)

	The South End Newspaper - NATION/WORLD - Mathematician reaches 100k milestone for online integer archive (Site not responding. Last check: 2007-11-04)
		Mathematician reaches 100k milestone for online integer archive
		Anyone who spots an interesting sequence that’s not already in the database can send it in and get credit for it.
		The Online Encyclopedia of Integer Sequences is available online at http://www.research.att.com/~njas/sequences/index.html
	www.southend.wayne.edu /modules/news/print.php?storyid=553 (731 words)

	Open Directory - Science: Math: Number Theory: Software (Site not responding. Last check: 2007-11-04)
		Encyclopedia of Integer Sequences Seeker - EIS-Seeker is a libguile-based scheme interpreter devoted to the study of the Encyclopedia of Integer Sequences database.
		Factorizer - A Windows program to find all factors of any positive integer less than 2^31 - 1; decompose numbers into their prime constituents; find prime numbersand pairs of primes; and to plot Erdos-Kac and Palmen Color histograms.
		GNUBC - Supports arbitrary precision integer arithmetic calculations with interactive execution: it is a superior version of the basic bc program which comes with the UNIX operating system.
	dmoz.org /Science/Math/Number_Theory/Software (692 words)

	Online Handbook of Integer Sequences (Site not responding. Last check: 2007-11-04)
		The following description of server usage is based on N. Sloane's announcement in The Electronic Journal of Combinatorics, which you should consult for more information.
		There may be up to five such lines in a message.
		The program will automatically inform you of the first seven sequences in the collection that match each line.
	www.math.ufl.edu /math/sequences.html (65 words)

	Integer Complexity -- from Mathematica Information Center
		This notebook provides code to evaluate many different types of integer complexity.
		In the PlusMinus section is code that was used to disprove a conjecture listed in the Encyclopedia of Integer Sequences.
		Also, Stephen Wolfram's NKS Online, Page 916, discusses it.
	library.wolfram.com /infocenter/MathSource/5175 (78 words)

	Online Encyclopedias, Dictionaries and Glossaries - Science Library - University Libraries - USC
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		The Encyclopedia of Astrobiology, Astronomy and Space Flight
	www.sc.edu /library/science/encyclo.html (120 words)

	David Bunde Links (Site not responding. Last check: 2007-11-04)
		Links to online CS journals (Includes those above, but others as well.)
		Online Dictionary of Algorithms, Data Structures, and Problems
		ACM Technews a clipping service for online articles about computer science
	compgeom.cs.uiuc.edu /~bunde/links.html (176 words)

	Encylopedia of Mathematics
		MetaMath - has hierarchical proofs (expressed in a logic).
		"Prove or disprove 100 conjectures from the OIES" by Ralf Stephan - semi-automated conjecture generation using the Online Encyclopedia of Integer Sequences
		Son of BirdBrain - choose some axioms and a conjecture to be proven.
	math.stanford.edu /~dford/em/links.html (144 words)

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