Buy A Handbook of Integer Sequences on ✓ FREE SHIPPING on qualified orders. Cover for A Handbook of Integer Sequences N.J.A. Sloane If nothing is known about the history of the sequence or if it is an arbitrary sequence, nothing can. The On-Line Encyclopedia of Integer Sequences. Neil J. A. Sloane. Visiting Scholar, Rutgers University. President, OEIS Foundation. 11 South.
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Today I want to write about favourite sequences. It is just an ordered list of numbers whose terms can be described. For example, the prime numbers — the numbers that can only be divided by themselves and 1 — form a sequence:. Ok, so far, so predictable. Prime numbers and Fibonacci numbers are well known throughout general culture.
Mathematicians drool over this sequence, because of the pleasingly self-referential way it is defined. If we start at the sloahe of the sequence, then, as integr below, the length of the runs recreates the original sequence. In other words, the Kolakoski sequence describes the length of runs in the sequence itself. It is the only sequence that does this except for the same sequence with the initial 1 deleted.
The Kolakoski sequence is prestigious for another reason: The OEIS is one of the best-known mathematical databases on the web and this week it is the subject of a conference at Rutgers Universitytimed to coincide with its 50th birthday and the 75th birthday of its founder Neil Sloane.
Some people collect stamps, some collect fossils but Neil has always collected sequences. In the s he started to write his favourite ones on file cards.
He was only interested in integer sequences, which are those made up of whole numbers and negative numbers and zero. By he had 2, sequences, which were published as a book: A Handbook of Integer Sequences. Sfquences day mathematicians around the world send Neil new sequences, which are then approved or rejected for inclusion by him and his team of 20 editors-in-chief and associate editors.
The OEIS still grows by about 40 sequences a day. It is a marvellous resource, which gets about nine million hits a month, and it has turned Neil — who was born in Wales, brought up in Integrr and has spent his adult life in the USA — into the sequences superstar.
I caught up hanbook Neil via Skype and asked him whether he had any new favourite sequences from the last few years.
Neil Sloane: the man who loved only integer sequences
He mentioned a sequence submitted by Jan Ritsema Van Eck in The rule here is that you start with 0, and whenever you get to a number you have not seen before, the following term is a 0.
But if the number k has appeared previously in the sequence, then you count the number of terms since the last appearance of kand that number is the following term. And does every number eventually appear? Neil has lost none of his excitement about sequences.
This year he has already submitted more than sequences, bringing his total tally to more than 42, And when I come across a sequence I put it in the database. You can search for sequences by inputting numbers. So if you put in 0, 1, 1, 2, 3, 5 you will get the Fibonacci sequence, as well as more than others that also include these numbers.
Each sequence has its own page, which lists the early terms, and includes comments and references as well as other information. It also gives you the option to plot a graph of the sequence, or listen to it as a piece of music where each number is a note in a scale of eight octaves.
Mathematicians and scientists use the OEIS all the time.
Sometimes people go there because certain sequences crop up in their work, and it sllane the best place to see if other people have studied them.
It is also a badge of honour to get a og accepted — although Neil and the administrators tend to be very generous in their selection criteria. The OEIS is also a source of interesting problems, quite often that arise from the recreational mathematics community. In fact, one of the great strengths of the OEIS is wloane it unites professionals and amateurs. Jan Ritsema van Eck, of the above sequence, is not a mathematician but a geographer who works for the Dutch environmental assessment agency.
One prolific amateur is the Belgian journalist Eric Angelini, who is the author of the following sequence A submitted in July that Neil particularly likes:.
Neil Sloane: the man who loved only integer sequences | Alex Bellos | Science | The Guardian
The rule here is that if a vertical line is drawn in between any two digits, the number made up of the digits to the left is divisible by the single digit to the right. With the added constraint that numbers are not repeated and you always take the lowest number possible. She has the bed and ear-plugs for herself. Eric is a fan of the French literary movement Oulipoa group of mathematically inclined, predominantly French-speaking writers who use constrained writing techniques, such as writing a book without using the letter e.
The rule here is that the difference between each term is the number made by joining the digits either side of the comma between those respective terms. This visually produces a new integer C that is – guess what? An interesting fact about the commas sequence is that it carries on for an awfully long time.
It contains exactly 2, terms. You extract sieve out all the appearances of the prime numbers in the decimal expansion of pi. In other words, to be inventive in this medium, one must have mastery of only two things, numbers and ideas. Perhaps it is, but the OEIS sees to it that even the drivel of fools is harnessed industriously. If you have your own favourite sequences from the OEIS, please list them in the comments section with the reasons why. Thanks to Emma Ringelding for her illustration.
More of her art and cartoons here. For latest updates on this blog and other mathematical miscellany follow me on twitter and Facebook. For example, the prime numbers — the numbers that can only be divided by themselves and 1 — form a sequence: But have you ever heard of the Kolakoski sequence?
The sequence only contains 1s and 2s. They appear either in a run of one, or in a run of two. Topics Mathematics Science blog network.
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